MATH 1780 Lecture Notes Chapter 3 Section 2

MATH 1780 Lecture Notes Chapter 3 Section 2 - Consider a...

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Unformatted text preview: Consider a game in which you toss two coins, if the two coins match then you win $1; if they do not match you lose $1. In the long run, how much would you expect to win or lose? Solution: Since the chances of winning equal the chances of losing, on average you would expect to win (1/2)(1) + (1/2)(-1) = $0. The expected value of a discrete random variable X with probability distribution p(x) is given by Where the sum is taken over all possible values of x for which p(x) > 0. We will sometimes use the notation E(X) = . Theorem: If X is a discrete random variable with probability distribution p(x) and if g(x) is an real valued function of X, then = x x xp X E ) ( ) ( = x x p x g X g E ). ( ) ( )) ( ( Consider the coin tossing game again, only this time suppose you win $1 if the match is tails, $2 if...
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MATH 1780 Lecture Notes Chapter 3 Section 2 - Consider a...

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