please type in your hand clearly so I can understand the formula and explanation thank you  Consider the following game. A fair coin is flipped until the first tail appears; we win $2 if it appears on the first toss, $4 if it appears on the second toss, and in general  if it first occurs on the k-th toss. Let the random variable X denote our winning. How much should we have to pay in order for this to be a fair game? Note: A fair game is one where the difference between the ante and E(X) is 0

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.4: Expected Value
Problem 30E
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please type in your hand clearly so I can understand the formula and explanation thank you 

Consider the following game. A fair coin is flipped until the first tail appears; we win $2 if it appears on the first toss, $4 if it appears on the second toss, and in general  if it first occurs on the k-th toss. Let the random variable X denote our winning. How much should we have to pay in order for this to be a fair game? Note: A fair game is one where the difference between the ante and E(X) is 0  

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