Question

A class has 15 students whose ages are 14, 17, 15, 14, 21, 19, 20, 16, 18, 17, 20, 17, 16, 19 and 20 years respectively. One student is selected in such a manner that each has the same chance of being selected and the age X of the selected student is recorded. What is the probability distribution of the random variable X?

Answer 1

Here, X can take the values 14, 15, 16, 17, 19, 20 and 21.
Now,
$$\begin{gathered} P\left(X=14\right)=\frac{2}{15} \\ P\left(X=15\right)=\frac{1}{15} \\ P\left(X=16\right)=\frac{2}{15} \\ P\left(X=17\right)=\frac{3}{15} \\ P\left(X=18\right)=\frac{1}{15} \\ P\left(X=19\right)=\frac{2}{15} \\ P\left(X=20\right)=\frac{3}{15} \\ P\left(X=21\right)=\frac{1}{15} \end{gathered}$$

Thus, the probability distribution of X is given by

X	P(X)
14	$\frac{2}{15}$
15	$\frac{1}{15}$
16	$\frac{2}{15}$
17	$\frac{3}{15}$
18	$\frac{1}{15}$
19	$\frac{2}{15}$
20	$\frac{3}{15}$
21	$\frac{1}{15}$