1.You and a friend play a game where you each toss a balanced coin. If the upper
ID: 3073679 • Letter: 1
Question
1.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 $2; if the faces are both heads, you win $8; if the coins do not match (one shows a head, the other a tail), you lose $4 (win ($4)).Calculate the mean and variance of Y, your winnings on a single play of the game. Note that E(Y) > 0.
E(Y)
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?
$
2.Each of three balls are randomly placed into one of three bowls.
Find the mean and standard deviation for Y = the number of empty bowls. (Round your answers to two decimal places.)
=
=
What is the probability that the value of Y falls within 2 standard deviations of the mean?
Explanation / Answer
1)
Y = 2 when TT
= 8 when HH
-4 when HT or TH
probability of each HH,TH,HT, TT = 1/4
hence
Y = 2 with p = 1/4
= 8 with p = 1/4
= -4 with p = 1/2
hence
E(Y) = 1/4 (2 + 8 ) + 1/2 (-4)
= 2.5 - 2 = 0.5
E(Y^2) = 0.25 * 2^2 + 0.25*8^2 + 0.5 * (-4)^2
= 25
Var(Y) = E(Y^2) - (E(Y))^2
= 25- 0.5^2
= 24.75
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