Question

The random variable x represents the number of boys in a family with three children.
Assuming that births of boys and girls are equally likely, find the mean and standard
deviation for the random variable x.

Answer 1

This is a binomial distribution with parameters
n=3 (number of trials in the experiment)
p=1/2 (probability of boys, X)
q=1-p (probability of girls)

For a random variable X with a binomial distribution (n,p,q), then
E(x)=μ=np
σ²=npq
where σ=standard deviation (of population)