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Math Help - Find E(X)

  1. #1
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    Find E(X)

    In a state lottery a three digit integer is selected at random. A player bets $1 on a particular number and if that number is selected, the payoff is $500 minus the $1 paid for the ticket. Let X equal the payoff to the bettor, namely -$1 or $499, and find E(X).
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    Quote Originally Posted by jennifer1004 View Post
    In a state lottery a three digit integer is selected at random. A player bets $1 on a particular number and if that number is selected, the payoff is $500 minus the $1 paid for the ticket. Let X equal the payoff to the bettor, namely -$1 or $499, and find E(X).
    The numbers start from 001 and end at 999. So there are 999 numbers.

    Therefore Pr(X = -1) = 998/999 and Pr(X = 499) = 1/999.

    Calculate E(X) in the usual way.
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    Is E(X) then (-1*999)+(499*1)=499-999 = -500? Thank you for your help.
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    Quote Originally Posted by jennifer1004 View Post
    Is E(X) then (-1*999)+(499*1)=499-999 = -500? Thank you for your help.
    No, the expected pay off is:

    (-1)Pr(-1)+(499)Pr(499)=-1(998/999)+499(1/999)

    and a simple reality check should tell you that the expected pay-off is of the order of -0.5.

    Also the wording of the original problem is vague and inplausible so double check it.

    CB
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    That is the way the problem is worded. All problems in my text seem to be vague. Would the pribabilities actually be 999/1000 and 1/1000 since 0 0 0 would also be considered a three digit integer? This would then make E(X)=-1/2 rather than -.4995

    Thank you for your help!
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    Quote Originally Posted by jennifer1004 View Post
    That is the way the problem is worded. All problems in my text seem to be vague. Would the pribabilities actually be 999/1000 and 1/1000 since 0 0 0 would also be considered a three digit integer? This would then make E(X)=-1/2 rather than -.4995

    Thank you for your help!
    If you want to include 000 then the probabilities change. It should be simple to make the necessary changes and calculate the new answer.
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    I think my answer would just be -1/2
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    Quote Originally Posted by jennifer1004 View Post
    I think my answer would just be -1/2
    Correct.
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