Question

Mark the correct alternative in the following question:

For the following probability distribution:

X:	1	2	3	4
P(X):	$\frac{1}{10}$	$\frac{1}{5}$	$\frac{3}{10}$	$\frac{2}{5}$

The value of E(X²) is

(a) 3 (b) 5 (c) 7 (d) 10

Answer 1

The probability distribution of X is given below:

X:	1	2	3	4
P(X):	$\frac{1}{10}$	$\frac{1}{5}$	$\frac{3}{10}$	$\frac{2}{5}$

$$\begin{gathered} \mathrm{E}\left(X^2\right)=1^2\times \frac{1}{10}+2^2\times \frac{1}{5}+3^2\times \frac{3}{10}+4^2\times \frac{2}{5} \\ =\frac{1}{10}+\frac{8}{10}+\frac{27}{10}+\frac{64}{10} \\ =\frac{100}{10} \\ =10 \end{gathered}$$

Hence, the correct alternative is option (d).