A roulette wheel has numbers from 1 to 36 and two "special" numbers 0 and 00....

A roulette wheel has numbers from 1 to 36 and two "special" numbers 0 and 00. A $1 bet on a number will pay $36 if that number comes up. It is also possible to bet on two adjacent numbers, with a $18 payout if one of them spells, or four adjacent numbers, with a $9 payout.

a) Let X be the total payout of a $1 bet on a number. Find E(X) and Var(X).
b) Let Y be the total payoff of a $1 bet on two adjacent numbers. Find E(Y ) and Var(Y ).
c) Let Z be the total payoff of a $1 bet on four adjacent numbers. Find E(Z) and Var(Z).
d) As a general rule, a $1 bet that will win in ''n'' out of 38 will pay 36/n $ . Find the mathematical expectation and variance of the total payoff of a $1 bet that would win in ''n'' cases.

Expert Solution

Part a

part b and c

Here I have assumed that either if one ,two or three or all of the adjacent chosen number come then also it could be considered a win.

orchestra answered 2 years ago

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