Question

The number of eggs X laid by an insect is known to have a binomial distribution with

parameter n and p.(0<p<1) . Each egg laid has a probability of hatching independently

of the development of any other eggs.

(a) Show that the number of eggs hatched has a binomial distribution

(b) What does this mean?

(c) What is the mean and variance of the number of eggs hatched?

Answer 1

The number of eggs laid is a binomial since the are two outcome, the probability of egg being laid is fixed(p),there is a fixed number of trials (n) and eggs are laid and hatched independently of each other.

Thus the number of eggs laid follows a binomial distribution.

mean =$n\cdot p$

variance=$\sqrt{n\cdot p\cdot(1-p)}$