Suppose that the number of customers who enter a post office

Suppose that the number of customers who enter a post office is a poisson random variable, and suppose that P{x=0}=0.05. Determine the mean and variance of X.

Solution

Let ? be the parameter of the poisson distribution

now, P(X = 0) = ?⁰ * e^-? / 0! = e^-? = 0.05

Therefore,

? = ln(100/5) = 2.996

Now ,

mean = ? = 2.996

variance = ? = 2.996