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Math Help - Sequence of coin tosses.

  1. #1
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    Sequence of coin tosses.

    A sponsor provides two prizes for a raffle. The first prize winner gets to
    choose a probability p \in [1/e, 1 − 1/e]. A sequence of independent coin flips with probability p for a head are then made. The winner receives 10 for each flip up to and including the first head. The same coin is tossed in another independent
    sequence and the second prize winner receives 5 for each flip up to and including
    the first head in this sequence.
    (i) Write down the probability mass functions of the amounts of the two payments
    U for the first prize and V for the second prize.

    For U, I was thinking along the lines of letting X_1,X_2,...X_N be Bernoulli variables and letting N be a different random variable but couldn't quite get this to work. Could someone start me off?
    Last edited by mr fantastic; June 26th 2011 at 12:09 PM. Reason: Re-titled.
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  2. #2
    MHF Contributor
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    Re: Probability Question

    The probability of the first head occuring on the n'th trial is

    P(n-1 tails in a row) * P(head)

    In which case the prize value is 10*(n).

    see if you can continue
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