Answer: 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