Question

Tutoring - On average there are 4 murders every week in the metropolitan area. What is the probability that there is at least one murder every other day in the metropolitan area? What is the probability that there are none?

Answer 1

let x be a random variable denote the number of murders every day. therefore x will follow poisson distribution with parameter lemda = 4/7 murder/day. therefore

P(X=x) = e^(-lemda) *lemda^(-x) /fact(x), x=0,1,2,...,hence

(a) at least one murder is 1-P(X=0) = 1-0.56(on putting x and lemda above)

=0.44

(b) P(X=0) = 0.56

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