The Winnipeg Rangers hockey team is considering a one-time charitable program fo

Question

The Winnipeg Rangers hockey team is considering a one-time charitable program for making a donation to the Winnipeg Children’s Hospital. The donation will be related to the number of goals the Rangers score in their next game. The team actuary has determined that the number of goals per game scored by the Rangers has a Poisson distribution with a mean of 3 goals per game. The proposed contribution is K times the number of goals, subject to a maximum of 3 goals. Find the value of K that would make the Rangers’ expected donations for a game be $5000.

Explanation / Answer

Here, if number of goals scored is X and X have poisson distribution

Pr(0 Goal) = POISSON (X = 0; 3) = 0.0498

Pr(1 Goal) = POISSOn (X = 1; 3) = 0.1494

Pr(2 Goal) = POISSON (X = 2; 3) = 0.2240

Pr(3 or more Goal) = POISSON (X >=3 ; 3) = 0.5768

Here, Expected number of Goals = E(X) = 0.0498 * 0 + 1 * 0.1494 + 2 * 0.2240 + 3 * 0.5768 = 2.3278

Proposed contribution or expected donation E(D) = K * Expected number of goals = K * 2.3278

Now value of K that would make the Rangers' Expected donation = 5000/2.3278 = 2148

so K is 2148.

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