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 $1; 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 $3 (win (−$ calculate the mean and variance of y, your winnings on a single play of the game. note that e(y) > 0.

 The mean and variance of Y is $0.25 and $6.19 respectively.

Step-by-step explanation:

Given : You and a friend play a game where you each toss a balanced coin.

sample space for tossing two coins : {TT, HT, TH, HH}

Let Y denotes the  winnings on a single play of the game.

You win $1; if the faces are both heads

then P(Y=1)=P(TT)=

You win $6; if the faces are both heads

then P(Y=6)=P(HH)=

You loose $3; if the faces do not match.

then P(Y=1)=P(TH, HT)=

The expected value to win : E(Y)=

Hence, the mean of Y : E(Y)= $0.25

Variance =

Hence, variance of Y = $ 6.19