Suppose a coin is tossed repeatedly until it falls heads. Let X be
the number of tosses necessary. Find the generating function of
X.

Question

Suppose a coin is tossed repeatedly until it falls heads. Let X be 
the number of tosses necessary. Find the generating function of 
X.

anonymous · Answer

i know generating functions are P(X=0) + P(X=1)z + P(x=2)z^2 + ... but i can't seem to be able to apply it to this question. maybe it's something to do with bernoulli trials?

dumbcow · Answer

so this will be a geometric distribution right

anonymous · Answer

yeah that's what i'm coming at something like f(z) = pz/(1-qz) but i'm not sure

dumbcow · Answer

http://en.wikipedia.org/wiki/Geometric_distribution#Moments_and_cumulants look at moment generating function p = 1/2

anonymous · Answer

ah finally got it just had to plug in p into p/(1-qz) with p = .5 and q = .5 and got 2/(2-z) which is right according to the book. lol i think i was over thinking it

dumbcow · Answer

haha yeah

anonymous · Answer

can u please write out the steps because i still don't understand