Question

The mean and variance of a random variable having a binomial distribution are 4 and 2 respectively, then P(X = 1) is ______.

Options

• `1/32`

• `1/16`

• `1/8`

• `1/4`

Answer 1

The mean and variance of a random variable having a binomial distribution are 4 and 2 respectively, then P(X = 1) is `underlinebb(1/32)`.

Explanation:

Mean = np = 4    ...(1)

Variance = npq = 2    ...(2)

From (1) and (2):

`(npq)/(np) = 2/4`

∴ q = `1/2`,

p = `1 - 1/2 = 1/2`

From (1):

`n(1/2)` = 4,

∴ n = 8

∴ P(X = 1) = `""^8C_1(1/2)(1/2)^7`

= `8 xx 1/(2)^8`

= `1/32`