Question

Let X ~ B(n, p) if E(X) = 5, Var(X) = 2.5, then p(X < 1) is equal to ______.

विकल्प

• `(1/2)^11`

• `(1/2)^10`

• `(1/2)^6`

• `(1/2)^9`

Answer 1

Let X ~ B(n, p) if E(X) = 5, Var(X) = 2.5, then p(X < 1) is equal to `underlinebb((1/2)^10)`.

Explanation:

Here, mean E(X) = 5

and variance, Var (X) = 2.5

`\implies` np = 5 and npq = 2.5

`\implies`  5q = 2.5

`\implies` q = `1/2`

Also, p + q = 1

p = 1 – q

`\implies` p = `1 - 1/2`

= `1/2`   ...[∵ np = 5]

`\implies n xx 1/2` = 5

`\implies` n = 10

 p(X < 1) = p(X = 0) = ⁿC_rp^rq^n–r

= `""^10C_0(1/2)^0(1/2)^(10 - 0)`

= `1 xx 1 xx (1/2)^10`

= `(1/2)^10`