Discussion
Find the variance in uniform distribution if X is uniformly distributed over (5, 30)?
Answer: B
The variance is 52.083.
For a uniform distribution on (a, b) the variance is \((b-a)^{2}/12\):
\[ \frac{(30 - 5)^{2}}{12} = \frac{625}{12} \approx 52.083 \]
17.5 is the mean, \((5 + 30)/2\), not the variance, and 1/5 and 85.052 do not come from the formula.
For any uniform distribution the mean is the midpoint (a + b)/2 and the variance depends only on the width b - a, so shifting the interval does not change the variance.
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