Question

In a valid probability distribution, each probability must be between 0 and 1,inclusive, and the probabilities must add up to 1. If a probability distribution is1/10 1/5 1/2 x what is the value of x?

Answer 1

SOLUTION:

All probabilities must add up to 1, thus;

$\frac{1}{10}+\frac{1}{5}+\frac{1}{2}+x=1$

Solving, we have;

$\begin{gathered} \frac{1}{10}+\frac{2}{10}+\frac{5}{10}+x=1 \\ \frac{8}{10}+x=1 \\ x=1-\frac{8}{10} \\ x=\frac{2}{10}=\frac{1}{5} \\ \end{gathered}$

Thus, the answer is 1/5