QUESTION

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10 An instant lottery ticket is purchased for $\$ 2$. The possible prizes are $\$ 0, \$ 2, \$ 20, \$ 200$ and $\$ 1000$. Let $Z$ be the random variable representing the amount won on the ticket. $Z$ has the distribution: \begin{tabular}{|l|c|c|c|c|c|} \hline $\boldsymbol{z}$ & 0 & 2 & 20 & 200 & 1000 \\ \hline $\mathbf{P}(\boldsymbol{Z})$ & & 0.2 & 0.05 & 0.001 & 0.0001 \\ \hline \end{tabular} a Determine $\mathrm{P}(Z=0)$. b Determine $\mathrm{E}(Z)$ and interpret its meaning. c How much should you expect to gain or lose on average per ticket?

Public Answer

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