Suppose that the number of customers who enter a post office

Suppose that the number of customers who enter a post office in a 47-minute period is a Poisson random variable and that P(X = 0) = 0.02. Determine the (a) mean and (b) variance of X.

Solution

A)

For a Poisson variable,

P(x) = u^x e^(-u) / x!

Thus, as P(x = 0) = 0.02, then

P(0) = u^0 e^(-u) / 0! = 0.02

e^(-u) = 0.02

u = -ln(0.02) = 3.912023005 [ANSWER, MEAN]

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b)

As for Poisson variables, the mean and variance are the same,

variance = u

Then

variance = 3.912023005 [ANSWER]