Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2018 / Paper 2 / 14 / a / i

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- Solution i

Solution

Distinguish the production type as well as the stopping position. The sample space has the six outcomes

Ω = {G \cap x_{0}, G \cap x_{1}, G \cap x_{2}, D \cap x_{0}, D \cap x_{1}, D \cap x_{2}} .

Here

x_{k}

in an event means

X = x_{k}

. Their joint probabilities are

p g_{k}

and

(1 - p) d_{k}

, respectively. The conditional stopping laws obey

\sum_{k = 0}^{2} g_{k} = \sum_{k = 0}^{2} d_{k} = 1

; with the stated strict positivity all six outcomes are possible.

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