Calculating Expected Value - Michigan State University

17 Expected 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 O1O2O3X1X2X329 Fair Games; Expected Value is 0In a fair game,E = p(win)*winnings +p(lose)*loss = 0 Example: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?

Or, you get 1 point for each correct answer, and –(1/4)pt for each incorrect answer. 16 100 Questions Multiple Choice Test– 5 foils, different scoring “Your grade = # of correct answers - (1/5)(# of incorrect answers)” Suppose you guess at the answer to all 100 questions. What is the expected grade for the test? Per question:

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