# flips of coin

• Dec 30th 2009, 11:16 PM
qwerty321
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
• Jan 1st 2010, 06:14 AM
qwerty321
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
• Jan 1st 2010, 01:36 PM
ANDS!
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.