Question

Messages arrive to a computer server according to a Poisson distribution with a mean rate of 10messages per hour.

a) What is the probability that hte first message arrives in the first 5 minutes? (randome variable time)

b) What is the probability that 3 messages arrive in 20 minutes? (random variable # of messages)

Answer 1

a)
lambda = 10 per 60 mins

For 5 mins, lambda = 10/12

Here, λ = 0.8333 and x = 1
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X = 1)
P(X = 1) = 0.8333^1 * e^-0.8333/1!
P(X = 1) = 0.3622
Ans: 0.3622

b)
for 20 mins, lambda = 10/3 = 3.33

Here, λ = 3.3333 and x = 3
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X = 3)
P(X = 3) = 3.3333^3 * e^-3.3333/3!
P(X = 3) = 0.2202
Ans: 0.2202