### Home > PC3 > Chapter 12 > Lesson 12.3.1 > Problem12-129

12-129.

Consider the discrete random variable $X$ with the following distribution.

 $X$ $5$ $6$ $8$ $12$ $P(X)$ $0.2$ $0.1$ $0.3$ $0.4$
1. Explain why this is a valid probability model.

In a valid probability model, the sum of the probabilities of the outcomes must be $1$. Also, the probability of each outcome must be between $0$ and $1$, inclusive.

2. Create a relative frequency histogram for this probability distribution.

3. Calculate the expected value of $X$.

$5(0.2) + 6(0.1) + 8(0.3) + 12(0.4)$