we flip a fair coin n times,if k is the number of 'heads' we get,we then flip the coin until we get k+1 heads(the number of flips is not given for the second round),let Y be the number of flips(for the second round)
determine the mean of Y.
here's my logic:
for the first round,this is a bionomial disribution so the mean is:np=n/2
for the second time,we need to get k+1 heads so the mean for the first k heads
is just like before: n/2..and to get the "extra" heads we need to add 2
so the mean is n/2 + 2
now here comes the tricky part..if I add those two i.e n/2 + (n/2 +2 ) = n+2
I get the right answer...but I dunno if it's correct,or why am I allowed to do that.
thanks for your help.