 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-2/14/c/i/solution

The intended season calculation needs the additional assumption that scores in different games are independent random variables. The printed statement gives their common one-game distribution but does not explicitly state independence; identical marginals alone do not determine season probabilities.

1 - P (X = 0) = 1 - e^{- λ}

of at least one goal, so

P (at least one goal in every game) = (1 - e^{- λ})^{10} .

Without independence this product is not determined by the supplied marginal distribution.

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