Alfred and Bertie play a game, each starting with \$100. Two fair dice are thrown. If the total scor

Question

Alfred and Bertie play a game, each starting with \$100. Two fair dice are thrown. If the total score is 5 or more, then Alfred pays \$$x$, where $0 If the total score is 4 or less, then Bertie pays \$$\left( x+8 \right)$ to Alfred. Show that the expectation of Alfred’s cash after the first game is \$$\frac{1}{3}\left( 304-2x \right)$. Find the expectation of Alfred’s cash after 6 games. Find the value of $x$ for the game to be fair, i.e. for the expectation of Alfred’s winnings to equal the expectation of Bertie’s winnings. Given that $x=3$, find the variance of Alfred’s cash after the ${{1}^{\mathrm{st}}}$ game.

Accepted Answer

$27\dfrac{2}{9}$

N1993 P2 Q7

N1993 P2 Q7

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