Question

If X is a random variable with probability distribution as given below:

X	0	1	2	3
P(X)	2a	a	4a	3a

Then, the variance of X is ______ 

Options

• `25/29`

• `23/7`

• `24/27`

• `29/25`

Answer 1

`underline(29/25)`

Explanation:

The sum of all the probabilities in a probability distribution is always unity.

∴ 2a + a + 4a + 3a = 1

⇒ 10a = 1

⇒ a = `1/10`

E(X) = ∑x_i.P(x_i)

= `0(2/10) + 1(1/10) + 2(4/10) + 3(3/10)`

= `9/5`

Var(X) = E(X²) - [E(X)]² 

= `0^2(2/10) + 1^2(1/10) + 2^2(4/10) + 3^2(3/10) - (9/5)^2`

= `29/25`