Question

Solve the following problem :

Find the expected value and variance of the r. v. X if its probability distribution is as follows.

x	1	2	3
P(X = x)	`(1)/(5)`	`(2)/(5)`	`(2)/(5)`

Answer 1

E(X) = \[\sum\limits_{i=1}^{3} x_i\cdot\text{P}(x_i)\]

= `1(1/5) + 2(2/5) + 3(2/5)`

= `(1 + 4 + 6)/(5)`

= `(11)/(5)`

E(X²) = \[\sum\limits_{i=1}^{3} x_i^2\cdot\text{P}(x_i)\]

= `1^2(1/5) + 2^2(2/5) + 3^2(2/5)`

= `(1 + 8 + 18)/(5)`

= `(27)/(5)`

∴ Var(X) = E(X²) – [E(X)]²

= `(27)/(5) - (11/5)^2`

= `(14)/(25)`.