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vichka [17]
3 years ago
10

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 $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. how mucuh should you oay ti okay this game if your net winnings, the difference between the payoff and cost of playing, are to have mean 0?
Mathematics
1 answer:
Kipish [7]3 years ago
3 0

Answer:

E(Y) = $0.5

Var(Y)  = 14.25

you should pay the same amount  $0.5

Step-by-step explanation:

E(Y) =  = Σ(YP)

P = probability of each outcomes.

Var(Y) = ΣY^{2}p − (μ x μ)

E(Y) = (2 x 0.25) +(6 x 0.25) + (0.5 x (-3)) = $0.5

Var(Y) = (2^{2}\\x 0.25) + (6^{2} x 0.25) +(-3^{2} x 0.5) - (0.5^{2})

       = 14.5 - 0.25

Var(Y)  = 14.25

for the difference between the payoff and cost of playing to have mean 0, you should pay the same amount  $0.5

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