Paper 2, Section II, F

Probability | Part IA, 2010

(a) What does it mean to say that a random variable XX with values n=1,2,n=1,2, \ldots has a geometric distribution with a parameter pp where p(0,1)p \in(0,1) ?

An expedition is sent to the Himalayas with the objective of catching a pair of wild yaks for breeding. Assume yaks are loners and roam about the Himalayas at random. The probability p(0,1)p \in(0,1) that a given trapped yak is male is independent of prior outcomes. Let NN be the number of yaks that must be caught until a breeding pair is obtained. (b) Find the expected value of NN. (c) Find the variance of NN.

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