Question

Throw a single die and let the random variable X be the number on the die. construct the probability distribution including possible value of X and find the mean of the distribution.

Answer 1

There are $6$ possible outcomes. Since the events are equally likely than

$$P(X=1)=P(X=2)=P(X=3)=P(X=4)$$

$$=P(X=5)=P(X=6)=1/6$$

Construct the probability distribution

$$\def\arraystretch{1.5} \begin{array}{c:c} x & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline p(x) & 1/6 & 1/6 & 1/6 & 1/6 & 1/6 & 1/6 \end{array}$$

$$mean=E(X)=1(\dfrac{1}{6})+2(\dfrac{1}{6})+3(\dfrac{1}{6})$$

$$+4(\dfrac{1}{6})+5(\dfrac{1}{6})+6(\dfrac{1}{6})=3.5$$