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Exercise
ABy Admin
May 02'23
Answer
Solution: B
Let [math]X[/math] be the number of burglaries. Then,
[[math]]
\begin{align*}
\operatorname{E}(X | X \geq 2) = \frac{\sum_{x=2}^{\infty}xp(x)}{1-p(0)-p(1)} &= \frac{\sum_{x=0}^{\infty}xp(x)-(0)p(0)-(1)p(1)}{1-p(0)-p(1)} \\
&= \frac{1-p(1)}{1-p(0)-p(1)} = \frac{1-e^{-1}}{1-e^{-1}-e^{-1}} = 2.39.
\end{align*}
[[/math]]
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