Answer: d. np(1 - p).
Step-by-step explanation:
Let x be any binomial variable which represents the number of success such that [tex]X\sim B(n, p)[/tex] , 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 :
[tex]E(x)=\mu=np[/tex]
[tex]Var (x)=\sigma^2=np(1-p)[/tex]
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) .
