Question

Find the variance and standard deviation of the random variable X whose probability distribution is given below :

x	0	1	2	3
P(X = x)	`1/8`	`3/8`	`3/8`	`1/8`

Answer 1

`x_i`	`p_i`	`p_ix_i`	`p_ix_i^2`
0	1/8	0	0
1	3/8	3/8	3/8
2	3/8	6/8	12/8
3	1/8	3/8	9/8
	Total	12/8	24/8 = 3

`E(X) = mu = sump_ix_i = 12/8 = 3/2`

`Var(X) = sum_(i=1)^n p_ix_i^2 - mu^2`

`= 3 - (3/2)^2`

`=3 - 9/4`

`= 3/4`

`∴ Var(X) = sigma^2 = 3/4`

Standard deivation of (X) = `sigma_x = sqrt(3/4) =sqrt3/2`