Question

Suppose electricity power failures occur according to a Poisson distribution with an average of 3 failures every twenty weeks. a) What is the probability there will be 5 failures in 10 weeks? b) What is the expected value of number of failures in 10 weeks? c) What is the variance in the number of failures in 10 weeks?

Answer 1

lambda for 10 weeks = 3/20 * 10 = 1.5

a)
Here, λ = 1.5 and x = 5
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X = 5)
P(X = 5) = 1.5^5 * e^-1.5/5!
P(X = 5) = 0.0141
Ans: 0.0141

b)
expected number of failures = 1.5

c)
variance = 1.5