Question

In a single throw of a die, a random variable X is defined as the prime number on its upper face. Find the variance of X.

Answer 1

In a single throw of a die, we get either no prime number or one prime number.

∴ X = 0, 1

x	P(x)	x2	xP	x2P
0	`1/2`	0	0	0
1	`1/2`	1	`1/2`	`1/2`

`sumxP = 1/2`

`sumx^2P = 1/2`

Variance = E(X²) – [E(X)]² 

= `(sumx^2P) - [sumxP]^2`

= `1/2 - 1/4`

= `1/4`