Question

In a single throw of a die, if X denotes the number on its upper face. Find the mean of X.

Answer 1

Clearly, X can take the values 1,2,3,4,5,6 each with probabilities $\frac{1}{6}$.

So, the probability distribution of X is as given below :

X : 1 2 3 4 5 6

P(X) : $\frac{1}{6}$ $\frac{1}{6}$ $\frac{1}{6}$ $\frac{1}{6}$ $\frac{1}{6}$ $\frac{1}{6}$

Therefore,

$\overline{X}=\frac{1}{6}\times 1+\frac{1}{6}\times 2+\frac{1}{6}\times 3+\frac{1}{6}\times 4+\frac{1}{6}\times 5+\frac{1}{6}\times 6$

$\overline{X}=\frac{1}{6}\times \frac{6(6+1)}{2}=\frac{7}{2}$