For the following probability distribution

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

E(X²) is equal to

Concept:

The expectation of a random variable E(X²) is given by \(\Sigma {x^2P(x) }\)

Calculation:

Given 

Expectation E(X²) is calculated by \(\Sigma {x^2P(x) }\)

⇒ E(X²) = \(\left(1^2\times\frac{1}{10}\right) +\left(2^2\times\frac{1}{5}\right)+\left(3^2\times\frac{3}{10}\right)+\left(4^2\times\frac{2}{5}\right)\)

⇒ E(X²) = \(\frac{1}{10}+\frac{4}{5}+\frac{27}{10}+\frac{32}{5}\)

⇒ E(X²) = \(\frac{100}{10}\) = 10 

The value of E(X²) is equal to 10.

The correct answer is option 4.