Question

Messages arrive to a computer server according to a Poisson distribution with a mean rate of 10 per hour. Round your answers to four decimal places (e.g. 98.7654).

(a) What is the probability that 9 messages will arrive in 2 hours?
(b) What is the probability that 10 messages arrive in 75 minutes?

Answer 1

X ~ Poisson ()

Where = 10 per hour

P(X) = e^-X / X!

a)

For 2 hours , = 10 * 2 = 20

P( x = 9) = e^-20 * 20⁹ / 9!

= 0.0029

b)

For 75 min, = 10 * 75 / 60 = 12.5

P( X = 10) = e^-12.5 * 12.5¹⁰ / 10!

= 0.0956