Paper 2, Section II, F

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

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 $p \in(0,1)$ that a given trapped yak is male is independent of prior outcomes. Let $N$ be the number of yaks that must be caught until a breeding pair is obtained. (b) Find the expected value of $N$. (c) Find the variance of $N$.

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