1. ## 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

2. 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

3. 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.