Question

The weekly number of IED incidents along a convoy route is represented by a Poisson random variable X with a mean of 1.7 per 100 miles. What is the probability there will be either one or two IED incidents along this 100-mile route over a three week period?

Answer 1

This is the Poisson distribution where mean($\lambda$​) = 1.7 per 100 miles

Probability of either one or two IED incidents along this 100-mile route over a three week period = P(X=1) + P(X=2)

Now,

for 3 week

$\lambda$​=1.7*3=5.1

P(X = x) = $(e^{-\lambda }*\lambda ^{x})/x&!$

P(X = 1 or 2) = ( e^-5.1*5.1^1)/1!*(e^-5.1*5.1^2)/2!

P(X = 1 or 2)=0.03109+.07929=0.11038 .