CAIE S2 2015 June — Question 3

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2015
SessionJune
TopicPoisson Distribution
TypeExpectation and variance of Poisson-related expressions

3 In a golf tournament, the number of times in a day that a 'hole-in-one' is scored is denoted by the variable \(X\), which has a Poisson distribution with mean 0.15 . Mr Crump offers to pay \(
) 200$ each time that a hole-in-one is scored during 5 days of play. Find the expectation and variance of the amount that Mr Crump pays.