Question

At random variable X – B(n, p), if values of mean and variance of X are 18 and 12 respectively, then total number of possible values of X are ______.

Options

• 54

• 55

• 12

• 18

Answer 1

At random variable X – B(n, p), if values of mean and variance of X are 18 and 12 respectively, then total number of possible values of X are 55.

Explanation:

We have, mean = 18 and variance = 12

So, np = 18 and npq = 12

∴ `(npq)/(np) = 12/18 \implies q = 2/3`

Therefore, p = 1 – q = `1 - 2/3 = 1/3`

After putting, p = `1/3` in np = 8, we get

`n(1/3)` = 18

`\implies` n = 54

Hence, total number of possible values of X

= n + 1

= 54 + 1

= 55