Question

The number of calls received by and office every 30 minutes is a poisson random variable with a mean value of 5. Find the probability that:

a. No calls will be received in a given 30 minutes period?

b. Exactly for calls will be received in a given 30 minutes period?

Answer 1

Let X be the Poisson random variable with the mean equal to μ = 5 (calls per 30 min). Then we know the probability mass function of X:

$f(k) = P(X=k) = \frac{5^{k}e^{-5}}{k!}$

a.

$f(0) = P(X=0) = \frac{5^0e^{-5}}{0!} = \frac{1 \times 0.006737}{1} = 0.006737$

b.

$f(4) = P(X=4) = \frac{5^{4}e^{-5}}{4!} = \frac{3125 \times 0.006737}{24} = 0.8772$