SSB Odisha Lecturer 2016: Lecturer recruitment for non-government aided colleges, Statistics
Text of page 1
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TEST BOOKLET
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co - 2st20 (Turn over)
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1 Mr" Xwants to purchase a car but he 3. An unbiased coin is tossed until a
is confused to choose the one. The head is obtained orthe total number
probabilities that he will go for the of tosses is 7. lt is desired to
category B or category C cars are calculate probability of the event E
respectively 0.54 and 0.46. lf he that coin is tossed at least three
selects category B cars, he will buy times. ln this context read the
either Palio or lndica with respective following carefully:
probabilities 0.48 and 0.52. On the
(i) The total number of
other hand if he goes for category C,
mutually exclusive and
the probabilities of buyingAccent is
equally likely outcomes is
0.59 and that of lkon is 0.41.ln the
8.
light of the above information, which
car do you think Mr. X is most likely
(ii) The numberof varourable
outcomes to event E is 3.
to purchase ?
(A) Palio (iii) Probability of E is 3/8.
Choose the correct answer from the
(B) lndica
following
(C) Accent
(A) (i) is true but (ii) and (iii) are
(D) Ikon
false
2, !n tossing of a coin four times, the (B) (i) is false but (ii) nand (iii) are
events E,, and E, are mutually true
exclusive if : (C) Allaretrue
(A) E., : Getting at leasttwo heads (D) Allare false
and E, : Getting at most two
tails
4. ln a university 60% students are
male. 50% of the male students and
(B) E., : Getting at leasttwo heads
30% of the female students are
and E, : Getting at least two
smokers. lf a student is seen smoking,
tails
the probability that it is a female
(C) E., : Getting at least three
student is :
heads and E, : Getting at most
three tails
(A) Equalto 0.3
(D) E,, : Getting at least three (B) Less than 0.3
heads and E, : Getting at least
(C) Between 0.3 and 0.4
three tails (D) Morethan 0.4
co - 25120 (2) Contd
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5 There are three bags, each (B) lf a random variable X has all
containing 12 white and 8 black balls. or some of moments, even then
One ball is drawn from the first bag
its moment generating function
and placed in the second bag. Then
may not exist except only at one
a ball is drawn from the second bag
point
and placed in the third bag. Finally a
ball is drawn from the third bag. The
(C) lf a random_variable X has all
probability that the ball drawn is white or some of the moments and
is: moment generating function
(A) 12t20 exists, it will always generate
(B) 13t20 those moments which exists
(c) 12t21 (D) lf a random variable X has all
(D) 13t21 the moments, its moment
generating funotion M*(t)
6. ln a multiple choice test having m always exists for al! realt such
choices in each question, an
that lt l< to (some realpositive
examinee either knows the answer
number). -
with probability p or guesses with
probability (1 - p). The probability of 8. Consider the events A and B such
answering the question correctly is 1, that P (A) = *,, (t I A) = ]ano
if heknowstheanswerand 1/m, if he
P (A I B) =
guesses. lf an examinee answers a *.The random variables
X and Y are defined as :
question conectly, the probability that
he really knewthe answer is :
X(w) =1,ifweA
(A) mp(1 + mp) = 0, otherwise
(B) (m - 1)o/(1 + mp) and
(C) mp/(1 + (m - 1)o) Y(w)=f ifweB
(D) (m - 1)r/(1 + (m - 1)o)
= 0, otherwise
7. Which of the following is always Which of the following is true ?
true ?
(A) P(X=0nY=0)=5/8
(A) lf a random variable X has no
(B) P(X=QnY=1)=118
moments, its moment
generating function will never (C) P(X=1nY=0)=3/B
exist (D) P(X=1nY=1)=118
co - 25t20 (3) (Turn over)
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9" Which of the following GANNOT be 12. The joint probability mass function of
a probability generating function ? random variables X and Y
(A) s-3 (2 - s)-1
(B) (t - r1o) / 1o(1 - s) r(x,v)=&#$pY=0, 1,
(C) s/(2 + s)
......, x; x= 0, 1, ......
(D) 4-n (1+ 3s)n
The marginaldistribution of :
10. The distribution function of any (A) X and Y both are Poisson
random variable is : (B) X and Y both are binomial
S., : always right continuous (C) X is binomial and that of Y is
Poisson ,,
S, : may be discontinuous at (D) X is Poisson and that of Y is
countable number of points binomial
Sa : monotone non-increasing
13. { & } is a sequence of identitically and
Choose the correct answerfrom the independently distributed random
following: variables with finite fourth central
(A) S,, and S, are true but S. is moment. Then the sequence {Xn } :
false
(A) Obeys weak law of large
numbers only
(B) S, and S. are true but S, is (B) Obeys strong law of large
false numbers only
(C) Sr and S, are.true but S, is (C) Obeys both weak law and
false strong lawof large numbers
(P) Obeys central limit theorem
(D) S., and S, and S, all are true only
11. The probability mass function of a 14. A person aims to shot the centre
random variable X is given below: (taken as the origin of a co-ordinate
system (X, Y) of a circular target of
f(x) = xl15 ;X = 1, 2, 3, 4, 5
radius R. lf all points are equi-
= 0 ; otherwise. probableto be shotand he hits a point
(X, Y) inside the.target only ; then the
Then the conditional probability that
probability density function of (X, Y)
X lies between 1l2and 5/2 given that
is:
X is greater than 1 is :
(A) f (x' Y) = l for-R<x< Rand
(A) ffi - R.y.R
(B) 3t7 (B) f (x,Y) =1lnR2for-R<x<R
and - R.'y <R
(c) 2t15 (C) f(x,y)= 1 for * +rf .92
(D) 1t5 (D) f (x,y) =1lnR2 tor**f .R2
co - 25t20 (4) Contd.
Text of page 5
,.
15. The random variable (X, Y) has the Reason (R) : For proper choice of 'c' ,
joint probability density function F(x) is monotone and bounded
between 0 and 1.
r(x,v)=
{Y' , ffi:and-x<Y<x Select your answer from the following
Which of the following expressions codes:
give the correct value of k ?
(A) Both A and R is true and R is
2x correct explanation of A
s: k-1 :JJX*-v )dy dx (B) Both A and R is true but R is
0-x
not correct explanation ofA
22 (C) A is true but R is false
P k-l - JJrfr- y)dx dy +
0y (D) A is false but R is true
o2 17. { Xn } is a sequence of random
J J*f*-y)dx dy variable having the corresponding
-2-y sequence of c.d.f. { Fn },where
Choose your answer from the 0
following codes : if x < - n
[**n if -n<x <n
(A) Both S and P are false Fn(x) = 1 *
(B) Both S and P are true t ifx>n
1
(C) S is true but P is false
(D) S is false but P is true Then which of the following
statement(s) is (are) true ?
16. Read the following statements
Statement S : Xn Converges in
carefully in context of the function
distribution
given below:
Statement P :Xn Converges in
F(x)=o, ifx<0
probability
=3c2, if o<x< 1
Choose your answer from the
= 4c-7c2, if 1<x<2
following codes :'''
=9c-7c2-1, it2<x<3
=1, if 3< x.
(A) Both S and P are true
Assertion (A) : F(x) can be cumulative (B) S is true but P is false
distribution function of a continuous (C) Both S and P are false
positive random variable for properly (D) Fn(x) is nota welldefined c.d.f
chosen value of 'c'.
of any random variable
co - 25t20 (5) (Turn over)
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,. :'
18. Match the items in LstAwith those in (C) S is false but P is true
List B : (D) Both S and P are false
ListA (law of large number)
(l) . Weak Law of Large Number 20. Read the following statements
carefully in the context of the function
(l) : Strong Law of Large Number
given below:
(lD : CentralLimitTheorem
List B (Type of convergences)
q(t)=1-ltl, ifltl<1
(i) : Convergence in Law =Q , ifltlrt
(ii) : Convergence in Probability Assertion (A) : g(t) cannot be
characteristic fu nction of any random,
(iii) : ConvergenceAlmostSure
variable.
Choose the answer from the
Reason (R) : 9(t) is not continuous
following codes:
function of t.
(A) : i! i:i :
Select you r answer from the following
Iillll
codes:
(B) I li rlr
(A) Both A and R is true and R is
llllll
correct exptanation of A
(c) I ',l ili (B) Both A and R is true but R is
iltllt
not correct explanation ofA
(D) I ll ':' (C) BothAand R is false
llllll
(D) A is true but R is false
19. Considerthe following function :
21. Read the following statements care-
f(x, y) =2,for0 < x < 1 and 0 <Y < x. fully:
Statement S : f(x, y) is a joint S : Poisson distribution is
1
probability density function.
limiting case of Binomial
Statement P : The conditional distribution.
probability density function X given
S 2 : Poisson distribution is
Y isf*tv (, I y) = (1 -y)-1 ; o < x< 1
limiting case of Negative
Choose your answer from the Binomial d istribution.
following codes:
S : Geometric distribution is
(A) Both S and P are true 3
special case of Negative
(B) S is true but P is false of Binomial distribution.
co - 25t20 (6) Contd.
Text of page 7
Choose the conect answer from the (B) Both A and R is true but R is
following: not correct explanation of A
(A) S., and S, are true but S. is (C) A is false but R is true
false (D) A is true but R is false
(B) S, and S. are true but S., is
false
24. lf X.,, X2 and X3 are three
independent Poisson variables with
(C) S., and S, are true but S, is
false
parameters X1, X2 and 1,3
(D) S., and S, and S, all are true respectively, the conditional
distribution of X, X, and Xr, given
22. Mean is always less than variance that X., * X, * Xe = 100 is :
for: (A) Poisson
(A) NegativeBinomialdistribution (B) Binomial
only
(B) Geometric distributicin only '
(C) Hypergeometric
(C) Negative Binornial distribution (D) Trinomial
and Geometric distribution both 25. X is a standardnormal distribution.
(D) Neither Negative Binomiat Define
distribution nor Geometric
distribution x if xl 1
f= -x if xl
I
1
23. The joint probability densityfunction I
of (X, Y) is f(x, y) = exp { - (x + y) }, for
Then the distribution of Y is:
0 < x < ?11d 0 < y <
"" -. Read the
following statements carefully :
(A) Uniform over (0, 1)
Assertion (A) : P(X . Y I X < 2Y) =
(B) Uniform over (-1, 1)
P(X'y1' (C) Standard normal
Reason (R) : X and Y are inde- (D) Normal butotherthanstandard
pendently exponentially normal
distributed and 26. The t-distribution with one degree of
exponential distribution
freedom is :
possesses lack of
memoryproperty.
(A) Cauchy'sdistribution
Select your answerfrom the following
(B) Beta distribution of first kind
codes: (C) Beta distribution of second
(A) Both A and R is true and R is kind
correct explanation ofA (D) Normaldistribution
co - 25t20 (7) (Turn over)
Text of page 8
27. X is a Negative binomialvariablewith Assertion (A) : X and Y are binomially
parameter k and p. Then : distributed with
parameter(n, p) and (n, q)
1
1 respectively
tk-1
0(m,k) Jp Reason (R) : X and Y are dependent
having non-linear
1t -gm-1 ot regressions
Select your answer from the following
(B) P(X>m)=r*i*'/ codes:
(A) Both A and R is true and R is
11+ t;m*k dt correct explanation of A
1 (B) Both A and R is true but R is
1
not correct explanation ofA
B(m,k) Jtx-t
p
(C) Both A and R is false
(1 - t)m-1 dt (D) A is true but R is fatse
30. X and Y are independently identically
1 ?.rn-r distributed geometric random
(D) P(x<m)= p(rgl'
variables, each with parameter p.
The conditionaldistribution of X given
11+ t;m*k dt
X + Y = n (finite integer) will be :
28. For a Binomial distribution B (X | 20, (A) Binomialwithparameter(n. p)
p), the variance cannot exceed : (B) Binomial "with parameter
(A) 5 (n'1-p)
(B) 10 (C) Uniform with parameter n + 1
(D) Uniform with parameter n
(c) 20
(D) Nothing definite can be said 31. X has Hypergeometric distribution
with parameter (N, M, n). lf N + ""
29. The joint distribution of X and Y is such that M/N -+ 6, then the limiting
f*,r(r, y) = [ n l{x! y! (n -x-y)! }] p" distribution X would be :
qY (1-p-q)n-*-Yforx, y = 0, 1 ,2, .....,fl ,
(A) Poisson with parameter 6
x+ySn ; 0<p, q< 1 and p +q < 1. (B) Poisson with parameter n6
-Read the following statements (C) Binomialwith parameter (n, 6)
carefully: (D) Binomialwith parameter (M, n6)
co - 25t20 (8) Contd
Text of page 9
:t-...
32. The probability density function of X (C) 12: 15 . 10
is: (D) 12: 10 : 15
f(x) =
1
36. X has Beta distribution of first kind
nh**2\;-@<X(e with parameter5 (m, n) and Y is
Then, the distribution of f would be : independently distributed as Gamma
(A) N(0, 1) distribution with parameters (r, m + n), where m,
n, r > 0. The distribution of X + Ywill
(B) t-distribution
be:
(C) 12 distribution
(A) Beta of ,s'econd kind with
(D) F-distribution
parameters (m + r, n)
33. Variance of t-distribution with n (B) Beta of second kind with
degree of freedom is finite when : parameters (r, n)
(A) n=1 (C) Gamma with parameters
(B) 1<n<"o
(C) 1(n<"" (D) Gammawith parameters (r, n)
(D) n>3
37. X and Y are independent standard
34. Let U.,, U2, U, be independent normalvariables. Then the moment
identically distributed standard generating function of XYwillbe :
normal variables. lf X = U.,, Y =
(A) (1-() i,,
Ur * U, and Z= Ua i Uz* Ua, the
Cov (Y, Z) is closest to :
(B) (t -t2)12
(A) 1
(C) Exp(t2)
(B) 2
(D) Exp(2t2)
(c) 3 38. X and Y has the joint probability
(D) 4 density function f(x, y). The marginal
distribution g(x) of Xand h(y) of Yare
35. For normaldistribution with mean 10
normal. The covariance between X
and standard deviation 15, the ratio
and Y is zero. Then :
of mean deviation, standard
deviation and quartile deviation (A) f(x, y) mustbe bivariate normal
would be: and should'be equal to g(x) h(y)
(A) 10 : 12: 15 (B) f(x, y) must be bivariate normal
(B) 10:15: 12 but may nol beequalto g(x) h(y)
co - 25t20 (e) (Turn over)
Text of page 10
(C) f(x, y) may not be bivariate normal (B) Normal with:mean zero and
butshould be equalto g(x) h(y) variance2J
(D) f(x, y) may not be bivariate normal (C) Normal with m6an zero and
and may not be equalto g(x) h(y) variance 4o2
(D) Not normal distribution but
39. The jointprobability mass function of mixture of ,normal distribution
random variables X and Y
42. lf X has a F-distribution with (n, n2)
tr*"-l,Y(t - P1x-v degrees of freedom, the limiting
f(x,y) yffiy=0, 1, distribution of Y = C I Xwill follow a
chi-square distribution if :
....... x ; x= 0, 1, ...., ....
(A) C = n, ?rd n, -+"o
The marginaldistribution of :
(B) C = n., and n., -+ "o
(A) X and Y both are Poisson (C) C=nrandD24-
(B) X and Y both are binomial (D) C = nrand n, -+ oo
(C) X is binomial and that of Y is 43. X and Y are independently and
Poisson identically distributed chi-square,
(D) X is Poisson and that of Y is each with n degrees of freedom. The
binomial distribution of {n fl-Yy2{fi! is:
(A) Standard normal
40. lf X and Y are independent random
variables and each is uniformly
(B) Normal with mean zero and
variance 2n
distributed over(0, 1), then P (lX-Y I
< 0.5) is :
(C) twith n degrees of freedom
(A) Not more than 0.25 ' (D) twith 2n degree of freedom
(B) 0.50 44. X is a binomial variable with
parameter (n, p) and F is F-statistic
(c) 0.75
with (2k, 2(n - k + 1))degrees of
(D) More than 0.75 freedom. Then :
41. X and Y are independent random (A) P(X<k-1)= P(F>(n-k+ 1)
variables such that X is a normally p/k (1 - p))
distributed with mean zero and (B) P(X<k-1)= P(F<(n-k+ 1)
variance d and Y takes values + 1 p/k (1 - p))
or - 1 with equal probability. The (C) P(X<p-1)= P(F>(n-p+ 1)
distribution of S = XY + Xl/ is : up (1 - k))
(A) Normal with mean zero and (D) P(X<P-1)= P(F<(n-P+ 1)
variance d up (1 - k))
co - 25t20 (10) Contd.
Text of page 11
45. The heights (in nearest centimeters) 48. A reading test with maximum score
of a sample of ten PeoPle are : 67 73 50 yields a bell-shaped symmetrical
70 60 67 66 6871 70 67 . Which of the distribution with scores ranging from
following columns out of (a), (b) and 5 to 48 on a large sample of class Ill
(c) show the correct class limits ?
students. lf the same test is
administered to class V students, the
(a) (b) (c) (Frequency) frequency distribution is expected to
60.5-63.5 60-62 59.5-625 1
be?
63.5-66.5 63-65 625-65.5 0
66.5-@.5 66-68 65.5-68.5 5 (A) Positively skewed
@.5-725 69-71 68.5-715 3 (B) Negatively skewed
725-75.5 72-74 715-74.5 1
(C) Symmetricalandbell-shaped
(D) Symmetrical and bath tub-
(A) Column (a) and (b)
shaped
(B) Column (b) and (c)
(C) Column (a) and (c) 49. A precentile score of 40 of a student
(D) Allthe three columns in a test of total marks of 300,
indicates that he x :
46. The statistics defined as the distance
between 70th sample percentile and (A) Has answered 40% of the
30th sample percentile gives us the questions coLrectly in the test
information concerning :
(B) Knows 40o/o of the totaltopics
(A) Centraltendency
covered in the test
(B) Dispersion
(C) Skewness (C) Has earned a score equalto or
more than120.
(D) Kurtosis
(D) Hasearnddrascoreequaltoor
47 . lncreasing the frequencies in the tails
of a distribution will : betterthan 40% of the students
(A) Reduce the standard deviation who appeared in the test
(B) Not affect the standard devia- 50 Let X, X2...., Xn be i.i.d. standard
tion
normat variable-s and let Tn = (xf +
(C) lncreasethestandarddeviation
(D) Not affect the standard x;* .... + xf)ln:
deviation as long as'the (A) The limiting distribution of
increases are balanced on T-n - 1 is Chi-square with 1
each side of the mean. degree of freedom
co - 25t20 ( 11 ) (Turn over)
Text of page 12
(B) The limiting distribution of
where A is any
{n[n - 1) is Chi-square with 1 i>(^ -;)'
degree of freedom constant and x is the mean of the
numbers. Then
(C) The limiting distribution of
{n (Tn - 1) is normal with mean
(A) ,2 = o2
zero and variance 2 (B) s2, o2 l
(D) The limiting distribution of (C) s2 . o2
On- 1)dn is normalwith mean (D) s2.o2+A
zero and variance 2
54. 11 lxy denote the correlation ratio
51. Given the ultimate class frequencies between X and Yrespectively, which
(Ae1 = 250, (AB) = 120, (ctB) = 269 of the following is not true ?
and (crB) = 70, (cr) and (p) are : (A) rrr*ryx
(A) 450 and 370 (B) nfu=n?*< 1
(B) 370 and 450 (C) lnol=lq"rlS1
(C) 270 and 190 (D) r1*" is inddpendent of change
(D) 190 and270 of scale
52. A cyclist pedals from his house to his 55. ln a frequency table, the upper
college (which is 7 kms. away from boundary of each class is ktimes of
his house) at a speed of 10 , the lower boundary. X, and f, are the
kilometers per hour and returns back midpoint and corresponding
from the college to his house at 15 frequency of the ith (i = 1,2, ...., m)
kilometers per hour. His average class. N is the sum of all the
speed is:
frequencies. Then which of the
(A) 12.s following statg,,ments is/are true ?
(B) 12 Statement S : x. ='x.,kr'
(c) 13 Statement P : Geometric mean of the
(D) 11 .SX,'t)
data is
"ro('on*',
53. For n observations xl, \, ...., xn, let
Choose youl,answer from the
I
n
following codes :
l
S
2 1 (x -A)' and o2 =
n i=1
(A) Both S and P are true
co - 25120 (12) Contd.
Text of page 13
(B) S is true but P is false s2 : The mean and median for the
(C) S is false but P is true data will be,always differ if the
(D) Both S and P are false range for the data is 5.
56. The range of Karl Pearson's and Select the correct answer from the
Prof . Bowley's coeff icient of following codes
skewness are respectively : (A) Both S, and S, are true
(A) [- 3, 3] and [- 1, 1] (B) S,, is true but S, is false
(B) [- 1, 1]and [- 3, 3] (C) S., is false but S, is true
(C) [- 3, 3] and [- 3, 3] (D) Both S,, and S, are false
(D) [- 1, 1] and [- 1, 1]
59. Under usual notations, it is given that
57 . For a frequency distribution, a student r12= f 1g= 123= p, then :
calculated the value of P., and F, and
reported these as 0.97 and 1.78
(A) Rr.rs = p anq t12s= p
respectively. (B) R,.r. = p iZid11 + p) anci rrr.,
Assertion (A) : The student has = p ",12l r/1t + py
committed calculation (C) Rr.r. = p ^lzt.'l(1+ p) and rrr.u
mistake. =P/(1 +P)
Reason (R) : The value of p., can (D) R.,.rg = p I (1+ p) and 1123= p
neverto less than 1 lztllt+p)'
Select your answer from the following
codes: 60. Consider the equations of lines
(A) Both A and R is true and R is 3X+4Y=45and3X+Y=27.
correct explanation ofA
Choose your comment from the
following codes in thecontextof these
(B) Both A and R is true and R is
not correct explanation ofA
lines representing the pair of
regression lines:
(C) A is false but R is true
(D) A is true but R is false (A) The regression coefficientof Y
on X is -3l4
58. We have a data set consisting of 40 (B) The regression coefficient of Y
observations where an observation
can be either 5 or 10. Which of the
onXis-3
following statements are true ? (C) The correlation coefficient
S, : The mean and median for between X on Y is 1
the data will be same if the (D) These can never represent a
variance for the data is zero. pair of regression lines
co - 25t20 (13) (Turn over)
Text of page 14
61. Assertion(A) : The range of multiple (C) S and 1/M
correlation coefficient is (D) S and 1/(lvl- S)
[-1,+1]
63. lf X is a single observation from a
Reason (R) : Multiple correlation is
Poisson d istribution with parameter
simple correlation ),, consider the following in the
coefficient (which has the
context of estimation of exp(- 3),) :
range [ -1, +1] always)
between observed values
Assertion (A) : Unbiased
of a variable and its estimators may be
estimated values absurd.
calculated from a linear Reason (R) : (-3)x is the only
relation of the variable unbiased estimator of
with rest of the variables exp(- 3),).
determined by least Choose the answer from the
square method. following codes:
Select your answer from the following (A) Both A and R is correct and R
codes: is correct explanation ofA
(A) Both A and R is true and R is (B) Both A and R is correct and R
correct explanation of A
is not correct explanation ofA
(B) Both A and R is true and R is
(C) A is true but R is false
not correct explanation of A
(C) A is false but R is true (D) A is false.but R is true
(D) A is true but R is false 64. X is normally distributed with mean
zero and variance o2 and Y
62. A random sample X1, X2,...., Xn is
independently follows exponential
drawnfrom a population having p.d.f.
distribution with mean 2d. We wish
f(x I P, 0) = 0 exP [-0(x-P)l'
totest Ho : d S 1 against H, : d> 1
forx>p,e>0
at o percentlevelof significance. The
= 0, othewise.
uniformly most powerfut (UMP) test :
Let S be min(X 1,X2,...,.Xn) and M
(A) does not exist
be the sample mean. Then the MLE
of pand 0 are respectively:
(B) is a chi-square test
(A) S and M (C) is a t-test
':,
(B) SandM-S (D) is a F-test
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Text of page 15
65. A discrete random variable X has (C) J)ilr losxl"
probability mass function f(x | 0). On
the basis of a single observation, we (D)
;frl,'oo*'
wish to develop a test of size 0.05
for testing the hypothesis Ho : 0 = 0o 67. Let L denote the likelihood function
against H., : 0 = 0.,.The value of the and T be an unbiased estimator of
probability massfunction f(x | 0) under g(0). Then for K(e) > 0, T attains the
0 = 0o and 0 = 0., are given below: minimum variance bound if :
Value of the variable X = x (A) L = K(0) (r- g(e))
1234 (B) los L = K(e) (T-s(0))
f(x le/ .01 .04 .05 .e0 d
(c) log L = K(0) (T - g(e))
f(x le.,) .80 .10 .05 .05 .ie
Considerthe tests T., which rejects
&
Ho if x = 3 and T, which rejects Ho if (D) logL=K(e)(T-s(e))
@
x= 1or2.
(A) T., and T, both are having equal 68. tf X(1) . X(r) ( ...: ( X(n) b" ordered
size but different from 0.05
observations fiom thd following
(B) T, andTrbotharehavingequal
density function :
power
(C) T., ismorepowerfulthatT,
(D) T, is more powerfulthan T,,
f(x, o) =
),, *,rg. * < e + 1. The
66. Let X., , Xz, ......, Xn be a random maximum likelihood estimate will
sample from a Poisson distribution be:
with parameter p. What is the (A) X(,)
maximum likelihood estimate of
(B) X(n) :
e-nP? ,
(c) 2x(1)l x(n) +;
(A) t*)il,''
2X(r) + X(n)
(B)
s );:rxi (D)
3 .:|
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Text of page 16
69. Let, a random variable X follows the 72 ln sample from the population with
hyper geometric distribution will pmf : pdf:
1
n-x x ( x, Q (oo
PN(x) = = 0, 1,2, f(x, o) = ,,1.,1+ (x- t),], oo
n
The Cramer-Rao lower bound for an
.'",n unbiased estimator of 0 is :
On the basis of a single observation,
n
the MLE of N will be : (A)
2
(A) NM/x
(B) ?
(B) M /x n
(C) Nx/ M (c) t
2
(D) nMx
n
(D)
70. Let (X.,, Xr) be a random sample of 4
sizeZfrom N(0, e). lf, *=
73. Let x.,, xz, ....., Xn be a random
Y, sample from a uniform distribution
then unbiased estimatorof 202 is: on the interval (0, 0) then consider
(A) x2 the following :
(B) zxtx- rl (i) *(n) it the complete sufficient
(c) itzX- r) statistics for 0
(D) XtX - tt (ii) *(n) i. an unbiased estimator
for 0
71. Let X., , X2, ...., Xn be iid b (1 - 0)
random variables, 0 < e < 1. Then, /n+1\
iii) *(n) i. the asYmPto-
the estimator of 0 :
(
[;]
tically unbiased for0
nx+
J;
_ n+1
T(X) = 2 is (iv) ( n -,, is the UMVUE for
..G- )
e
(A) Both unbiased and consistent
(B) Unbiased but NOT consistent Which of the above statements ls/are
(c) Consistent but NOT unbiased correct ?
(D) Neither unbiased nor consistent (A) (i) and (iii) ep1,
co - 25t20 (16) Contd
Text of page 17
(B) (iv) only The uniformly most powerful(UMP)
test:
(C) (i), (iii) and (iv) only
(D) Allof the above
(A) Rejects Howhen X2 + Y sX'r,o
(B) Rejects Ho when X2 + Y 2X'r,,
74. When we are sampling from a (C) Rejects Howhen X2 + Y =X'*o
normal population with unknown (D) Rejects H6when X2 +Y rfr,o
mean p and unknown variance o2,
where x2n.o denotes the upper c
which of the following is a simple
percent point of chi-square
hypothesis ?
distribution with n degrees of freedom.
(A) Ho:p=10
77. LetX.,, &, .....,Xn be random sample
(B) Ho,tr=20,&=4 from normaldistiibution with mean 0
(C) Ho: o2 = 4 n
(D) Allthe three mentioned above anci variance 0. if T, =i E x, and
75. Which of the following is most n
correctly matched ? - tx?I
T2 -L,l r
i=1
(A) Fisher's - Uniformly
Factorization Most Power-
(A) T., and Trarejointly sufficient
Theorem fultest for 0
(B) RaoBlackwell - Minimum (B) Only T., is sufficient for 0
Theorem Variance un- (c) Only T, is sufficient for 0
biased Estima-
(D) Neither T.,,nor T, is sufficient for
tor
0
(C) Cochran' - lntervalEsti-
Theorem mation 78. The marks obtained by a group of
(D) MarkoVs - Sufficiency students are available in two
Theorem examinations. First one was held
before an extensive coaching and
76. X is normally distributed with mean
second one after the coaching. lt is
zero and variance o2 and Y known that marks are normally
independently follows exponential distributed. Even then '
distribution with mean 2d. W9 wish Statement (S) : We should use sign
to test Ho : d < 1 againstH,,: o2 > 1 test in ptace of paired t-
at a percent level of significance. test. .
co - 25t20 (17 ) (Turn over)
Text of page 18
Reason (R) : Sign test is more method. After completing the course,
powerful than paired t-test. students took a l.hourexam. Which
Choose your answer from the of the following is the correct degree
of freedom for an F-test for evaluating
following codes :
if the average test scores are
(A) S is true and R is its correct different for the different teaching
explanation methods ?
(B) S is true but R is not its correct (A) (5,45)
explanation (B) (5,44)
(C) S is false but R is true (c) (4,44)
(D) Both S and R are false (D) (4,40)
79. Wewishtoyou usea non-parametric 81. !f the coefficient,iof variation of the
test f6f testing the null hypothesis that study variable Y and the auxiliary
the given two independent sample variableX in a population are 18 and
come from same population. The 32 respectively, then forwhat range
populations may differ in their central
of the coefficient of correlation p
betweenXandY the ratiomethod of
tendency only. Which test should we
estimation will-be: preferable over
use ?
sample mean ?
(A) Sign test (A) p < 0.63
(B) Median test (B) 0.33<p<0.80
(C) Run test (C) p > 0.63 but less than 0.85
(D) Any of the above three (D) p>0.88 '',
80. A study compared five different 82. To examine whether two different
skin creams have different effects on
methods for teaching descriptive
the human body, n randomly chosen
statistics. The five methods were
persons were enrolled in a clinical
traditional lecture and discussion,
triat. CreamAwas applied to one of
programmed textbook instruction, the randomly chosen arms of each
porgrammed text with lectures person, cream B to the other. What
computer instruction, and' computer kind of design is this.?
instruction with lectures. 45 students (A) Completely Randomized
were randomly assigned, 9 to each Design
co - 25t20 (18) Contd
Text of page 19
(B) Balanced incomPlete block (C) - (1) + (a) - (b) + (ab) - (c) +
design (ac)-(bc) +(abc)
(C) Randomized block design (D) - (1)- (a) - (b) + (ab) + (c) +
(D) Latin square design (ac)-(bc)+(abc)
83. ln a survey of population consisting 85. An exhaustive list of all members of
of N = nk units, a sample of n units is
the population along with their
selected with a random staft between
identification particulars is called :
1 to k and then selecting every kth
unit. (A) Sampling design
Assertion (A) : The variance of the (B) Sampling frame
unbiased estimate of the (C) Population design
population mean cannot
(D) Population frame
be estimated.
Reason (R) : No unbiased estimate 86. ln a two way classification with one
of population mean observation per cell, there are 4 rows
exists. and 3 columns. The degrees of
Select your answer from the following freedom forthe error mean squares
codes: is:
(A) Both A and R is true and R is (A) 11
correct explanation of A
(B) Both A and R is true but R is
(c) 6
not correct explanation of A
(C) A is true but R is false (D) 3
(D) A is false but R is true 87 . ln sample suryeys, we can controlthe
84. Under usual notations, the effecttotal following to its minimum level:
IA ] in a 22-factorial experiment is (A) Onlysampling error
given by: (B) Only non-sampling error
(A) (1) + (a) - (b) + (ab) + (c) + (ac) (C) Total of sampling and non-
- (bc) + (abc) sampling errors
(B) - (1) - (a) - (b) (ab) + (c) + (D) Neither sampling nor non-
(ac)+(bc)+(abc) sampling errors
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Text of page 20
88. Read the following statements replications are as follows (in usual
carefully: notations):
S., . Systematic sampling is [1] = t8, [a] = 17, [b] = 25 and
partly probabilistic and partly labl = 39.
non-probabilistic. The sum of square due to interaction
S, : Systematic sampling AB is '.
provides unbiased estimates if (,q)6 :
there are some periodicfeature (B) 4
in the list of units.
(c) 3
Choose the correct answerfrom the
(D) None of the above
following:
(A) Both S,' and S, are true 92. For a Political Science class, it was
required to get opinion on free
(B) S, !s true but S, is false
primary education of members of a
(C) S., is false but S, is true particular party from a town. The
(D) Both S,, and S, are false town was divided into 17 blocks,
89. A Latin Square Design is a :
each with similar socio-economic
status distribution and other
(A) Completetwowaylayout
diversities. Rather than trying to
(B) lncompletetwowaylayout obtain a list of all members of that
(C) Completethreeway layout party of the town. lt was decided to
(D) lncompletethreewaylayout .select 3 blocks at random, using
simple random sampling without
90. In a 6 x 6 Latin Square Design with
replacement. For selected blocks,
two missing observations, the error
the list of all current members of the
and treatment degrees of freedom
party was collected from the block
are respectively:
office of the party. Then the opinion
(A) 18,3 on free primary education of the
(B) 18,5 members was collected. What kind
(c) 20,3 of design was used ?
(D) 20,5 (A) Simple random sampling
91. The responses in a factorial (B) Stratified sampling
experiment with factors A and B
(C) Systematicsampling
each at two levels with three (D) None of the above
co - 25120 (20) Contd
Text of page 21
93. ln randomized block design with k 95. The method of sampling used in the
treatments and two blocks with study is :
m ean e., and B, which one of the (A) Simple random sampling
following is the correct sum of the (B) Stratified random sampling
squares due to blocks ?
(C) Cluster sampling
(A) (Br - Ar)2t* (D) Conveniencesampling
(B) (Br - er)ztz*
(c) K(Br - Ar)2tz 96. The greatestweakness of this study
is:
(D) (Br - er)2tz
(A) The division of the sample into
Direction(Q, AIos, 94 to 96) : Refer to the two groups of 25
fo,llowing research situation : (B) The use of only 50 students in
A researcher who wanted to determine the the sample
behefits of using a new beginning algebra
(C) The use of stucients from oniy
study technique obtained permission from
one schoo!,.,
the school of a district to select students.
(D) The use of only two different
The researcher prepared a list of hlt
studytechniques
beginning algebra students of that school
and selected 50 out of them at random. 97. A random sample of size n is drawn
The researcher divided the students from a population of size N, having
randomly into two groups each consisting mean p and standard deviation o,
of 25 students, One group participated in using simple random sampling
the newstudy progpm and the othergroup without replacement. The covariance
was trained through the traditional study between any two sample
techniques. observation willbe :
94. The most likely target population in (A) -o2lN
this study is : (B) - o2 t(N -,1)
(A) Algebra students of the district (C) -o2 ln
towhich the school belong
(D) - o2 t(n - 1)
(B) All algebra students of that
schoolonly 98. Read the following statements
(C) Allatgebrastudents carefully in context of design of
experiment:
(D) Only the 25 students who
learned the new study 51 : Local control along with
techniques
replication diminishes the
error.
co - 25t20 (21) (Turn over)
Text of page 22
Sz , Local control along with 100. Assertion (A) : The total error in
randomization validates the sample surveys will be
error. more than that in
Choose the correct answerfrom the complete enumeration.
following'. Reason (R) : ln sample surveys both
(A) Both S,, and S, are true sampling and non-
(B) S., is true but S, is false sampling errors occur
(C) S., is false but S, is true whereas incomplete
enumeration only non-
(D) Both S,, and S, are false
sampling errors occur
99 lf the degree of freedom forthe error Choose your answer from the
sum of squares in a Latin Square following codes:
Design is 6 then its order is : (A) Both A and R is true and R is
(A) 3x3 correct explanation of A
(B) 4x4 (B) Both A and R is true but R is
(C) 5x5 not correct explanation ofA
(D) 6x6 (C) A is true but R is false
(D) A is false but R is true
:.'' . .
llrlrllrtrrrttt
co - 25120 (22) Contd
Text of page 23
SPACE FOR ROUGH WORK co - 25t20 (23 ) (Turn over)
Text of page 24
SPACE FOR ROUGH WORK
J
ru
a
co - 25t20 (130) (24 ) StatisticsOfficial key not published for this paper.
Page 1 of 24
Source: State Selection Board. Question paper published by State Selection Board.