Probability a coin lands on head

[james2000]

For A coin that comes up heads independently with probability p on each flip what is the variance in the number of flips until the kth head appears ?

 

[LCKurtz]

James, nobody is going to work your homework problems for you. Finish filling out the form showing the relevant equations and what you have tried. Then someone will help you.

 

[james2000]

what form ?

 

[rsa58]

in order to get say r heads you need to flip the coin at least r times. thus for x>=r the number of possible ways to get r-1 heads in x-1 trials is (x-1)choose(r-1) without respect to order. on the xth trial we will get the rth success. thus since the trials are independent r of those trials have probability p for heads and x-r the remaining trials are all tails which have probability q = 1-p. we form the product of these total number of success and failures with the number of ways in which they may occur and we arrive at the negative binomial distribution. this distribution has a variance can you look it up and calculate it?

 

[berkeman]

what form ?

The Homework Help Template form that you are provided when you start a new thread here in the Homework Help forums. It has sections where you fill in the relevant equations, and where you show us your attempt at a solution.

It's the form you deleted when you started this thread, apparently.