Calculating Expected Value

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17Expected Value , E(X), of a random Variable XStart with an the Outcomes: O1, O2, ... OnWith each outcome is associated a probability :p1, p2, ..., pnand a Value of therandom variable, X, :X1, X2, ..., XnThe Expected Value of the random variable Xis, by definition:E(X) = p(O1)X1+ p(O2)X2+p(O3)X3+ .... +p(On)XnThe Expected Value is often denoted just by Expected Value ()-73 151112E = + + = 4244 Make a table like this oneOutcome probability Value of XHH 1/4 7HT or TH 1/2 3TT 1/4 -15 O1O2O3X1X2X329Fair Games; Expected Value is 0In a fair game,E = p(win)*winnings +p(lose)*loss = 0Example:Suppose for some game, p(win) = 2/6; p(lose) = 4/6If you lose, you pay $1; if you win other player pays you $DWhat should D be if the game is to be fair?=+ 24**(1)66ED==Set 02ED10Expected Value - Example The game costs $2 to play. You are dealt a poker hand.

1 7 Expected Value, E(X), of a Random Variable X Start with an Experiment. List the Outcomes: O1, O2, …On With each outcome is associated a probability: p1, p2, …, pn and a value of the random variable, X, : X1, X2, …, Xn The expected value of the random variable X is, by definition: E(X) = p(O1)X1 + p(O2)X2 +p(O3)X3 + …. +p(On)Xn The expected value is often …

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