Question Solved1 Answer You and a friend play a game where you each toss a balanced coin. If the upper faces on the coins are both tails, you win $7; if the faces are both heads, you win $6; if the coins do not match (one shows a head, the other a tail), you lose $3 (win (-$3)). Calculate the mean and variance of y, your winnings on a single play of the game. Note that E(Y) > 0. EY) = V(Y) = How much should you pay to play this game if your net winnings, the difference between the payoff and cost of playing, are to have mean 0?

IBHATI The Asker · Advanced Mathematics

Transcribed Image Text: You and a friend play a game where you each toss a balanced coin. If the upper faces on the coins are both tails, you win $7; if the faces are both heads, you win $6; if the coins do not match (one shows a head, the other a tail), you lose $3 (win (-$3)). Calculate the mean and variance of y, your winnings on a single play of the game. Note that E(Y) > 0. EY) = V(Y) = How much should you pay to play this game if your net winnings, the difference between the payoff and cost of playing, are to have mean 0?
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Transcribed Image Text: You and a friend play a game where you each toss a balanced coin. If the upper faces on the coins are both tails, you win $7; if the faces are both heads, you win $6; if the coins do not match (one shows a head, the other a tail), you lose $3 (win (-$3)). Calculate the mean and variance of y, your winnings on a single play of the game. Note that E(Y) > 0. EY) = V(Y) = How much should you pay to play this game if your net winnings, the difference between the payoff and cost of playing, are to have mean 0?
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you win $7gThe face ari both headso you win $69{:[" you loss p "3" ( "-3" win) "],[=>quad E(x)=" ? "],[y=$7" when TT "],[=$6" when "HH],[=$-3" when THOHT "]:}when Two coins are Tossed.Then sample space, ={HH,TT,HT,TH}Probability of HH=(1)/(6){:[",, s, TT "=(1)/(6)],[" Prob. \& TH, HT "f=(2)/(6)=(1)/(3)],[E(v)=(1)/(3)xx7+(1)/(3)xx6^((2)/(6))+(1)/(3)xx(3)],[=(7)/(3)+2-1],[{:[V(y)=E(V^(2))-(E(x))^(2),3],[,=[(1)/(3)xx(7)^(2)+( ... See the full answer