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Unformatted text preview: More Distributions e) Determine whether the payout has positive, negative or zero skewness. Only one value of X lies below the mean, and 5 values lie above the mean. This looks like positive skewness. Just to check (you don’t have to), I calculated the third moment of X (not Y, but the skewness will have the same sign). E(X
µ)3] = Σ (x
µ)3 P(x) – see column 10 in the table above. It’s positive f) If the entry fee is $5, what is the probability that a student will break even or net a profit from this game? (Now you do have to consider the entry fee.) The student will net a profit or break even if he gets one or more spades. P(OneOrMore) = 1 – P(ZeroSpades) = 1 – 0.370 = 0.630 So the game is not terrible; it’s just not in your favor. g) A student does not know how to calculate the expected value of this game, so he decides whether to enter by rolling a die. If the number is 5 or 6, he will enter twice; otherwise, he will not enter at all. What is the probability that he will break even or net a profit from this series of events? We first calculate the probability for breaking even when entering twice. The profit is the sum of the two games. The easiest way is to calculate the probability that the student will lose money. The events that could lead to this are listed below, with G1 indicating Game 1 and the following number indicating the number of paying...
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This document was uploaded on 03/06/2014 for the course CEE 202 at University of Illinois, Urbana Champaign.
 Spring '08
 Clark

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