What is the standard deviation for the pay-offs of a coin flipping game where you get 2 dollars if heads and lose 1 dollar if tails. How does the standard deviation change if the probabilities remain constant but the pay-off changes to 3 dollars for heads and lose 1 for tails. What is the generalized formula for standard deviation in a coin flip with given probabilities and pay-offs?

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#### Best Answer

Relevant Formula

Source: http://en.wikipedia.org/wiki/Standard_deviation

For pay-off of 2, -1 and probabilities of 50%/50%.

Expected value = 0.50*2+.50*-1 = .50

Variance = 0.50*(2-.50)^2 + 0.50*(-1-.50)^2 = 2.25

SD = 2.25^(1/2) = 1.5

For pay-off of 3, -1 and probabilities of 50%/50%.

Expected value = 0.50*3+.50*-1 = 1

Variance = 0.50*(3-1)^2 + 0.50*(-1-1)^2 = 4

SD = 4^(1/2) = 2

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