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Math Help - flips of coin

  1. #1
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    flips of coin

    Hello
    I need helo with this problem
    Flip n=8 fair coins and remoev all the headss that came up.flip the other remaining until each has come up heads.We want to find the pmf of Y the number of trials needed.Let Xi be the number of flips required to observe heads on coin i,i=1,2,3...8 then Y=max(X1,X2...X8).
    I want to show that P(Y<=y)=[1-(1/2)^y]^8

    I know the formula but i dono from where to get the 1-(1/2)^y

    i got the pmf of Xi and it is (1/2)^x then what shall i do?

    Thanks everyone
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  2. #2
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    ok i got it
    but now i need to know how to find E(Y)?
    and what happens to E(Y) as the number of coins is doubled

    thank you
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  3. #3
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    You find the expected value the same way you find any expected value: the sum of X*P(X=x) for all values of x. So whatever function you figured out above for Y, simply multiply that by all possible values of Y and their probability.

    For what happens to the mean, doubling your values will double your mean since this is a linear transformation on the mean.
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