Question

The probability distribution of a discrete random variable X is given as under:

X	1	2	4	2A	3A	5A
P(X)	`1/2`	`1/5`	`3/25`	`1/10`	`1/25`	`1/25`

Calculate: Variance of X

Answer 1

Now the distribution becomes

X	1	2	4	6	9	15
P(X)	`1/2`	`1/5`	`3/25`	`1/10`	`1/25`	`1/25`

E(X²) = `1 xx 1/2 + 4 xx 1/5 + 16 xx 3/25 + 36 xx 1/10 + 81 xx 1/25 + 225 xx 1/25`

= `1/2 + 4/5 + 48/25 + 36/10 + 81/25 + 225/25`

= 0.5 + 0.8 + 1.92 + 3.6 + 3.24 + 9.00

= 19.06

Variance (X) = E(X²) – [E(X)]²

= 19.06 – (2.94)²

= 19.06 – 8.64

= 10.42