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Math Help - binomial random variables :-/

  1. #1
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    binomial random variables :-/

    A scalper is considering buying tickets for a particular game. The price of the tickets is $75, and the scalper will sell them at $150. However, if she can't sell them at $150, she won't sell them at all. Given that the demand for tickets is a binomial random variable with parameters n = 10 and p = 1/2, how many tickets should she buy in order to maximize her expected profit?
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  2. #2
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    Just walk your way through it.
    Profit From Sale: 150 - 75 = 75
    Profit From No Sale: 0 - 75 = -75

    Buy 1
    Pr(Not Selling It) = ^10 = q
    Pr(Selling It) = 1 - q = p
    Expected Profit: p*(75) + q*(-75)

    Buy 2
    Pr(Selling Zero) = ^10 = q
    Pr(Selling 1) = 10*^10 = w
    Pr(Selling Both) = 1 - (q+w) = p
    Expected Profit: p*(150) + w*(0) + q*(-150)

    You can keep wandering down the entire Binomial distribution (a nice spreadsheet makes this relatively simple) or you can determine a more direct way if you are REALLY paying attention.

    Note: It is possible the right answer if greater than 10. I didn't really solve the problem, but I'd keep that in mind, just in case you need it.
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