Discussion
A random variable x has the following probability function :
| Values of x | 0 | 1 | 2 | 3 | 4 |
| P(x) | 0 | k | 2k | 2k | 3k |
What is the value of k ?
Answer: B
The value of k is 0.125.
The probabilities of all values of a random variable must add up to 1:
\[ \begin{aligned} 0 + k + 2k + 2k + 3k &= 1 \\ 8k &= 1 \\ k &= 0.125 \end{aligned} \]
0.166 is 1/6, which comes from missing one of the 2k terms and adding the rest to 6k. 0.100 and 0.150 would make the total 0.8 and 1.2, which cannot be the total of a probability distribution.
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