Question

The variance Var(x) for the binomial distribution is given by equation :

a. np(n - 1).
b. np(1 - np).
c. n(1 - p).
d. np(1 - p).

Answer 1

Answer: d. np(1 - p).

Explanation:

Let x be any binomial variable which represents the number of success such that
`X\sim B(n, p)` , where n is the sample size or the total number of trials and p is the probability of getting success in each trial .

Then, the mean E(x) and the variance Var(x) for the binomial distribution is given by equation :

`E(x)=\mu=np`

`Var (x)=\sigma^2=np(1-p)`

where n is the sample size or the total number of trials and p is the probability of getting success in each trial .

Therefore , the correct option is option d. np(1 - p) .