Question

The number of visitors to a webserver per minute follows a Poisson distribution. If the average number of visitors per minute is 4, what is the probability that: (i) There are two or fewer visitors in one minute? (2 points) (ii) There are exactly two visitors in 30 seconds? (2 points)

Answer 1

i)
Here, λ = 4 and x = 2
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X <= 2).
P(X <= 2) = (4^0 * e^-4/0!) + (4^1 * e^-4/1!) + (4^2 * e^-4/2!)
P(X <= 2) = 0.0183 + 0.0733 + 0.1465
P(X <= 2) = 0.2381

ii)
Here, λ = 2 and x = 2
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X = 2)
P(X = 2) = 2^2 * e^-2/2!
P(X = 2) = 0.2707
Ans: 0.2707