Question

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

Answer 1

Answer: d. np(1 - p).

Step-by-step 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) .