1. ## Negative Binomial

A fair coin is continually flipped until heads appears for the tenth time. Let X denote the number of tails that occur. Compute the probability mass function of X.

My very first question is, by "compute the probability mass function of x" are they just asking me to write out p(a) in equation form?

I took some notes on the problem at office hours, but I didn't really understand what the prof was doing:

P(X=x) where x= # of tails = total (or x) - 10 Why is this x-10?

P(total=n) ~ Neg Binomial(n;10;1/2) => ~ $\binom {n-1} {m-1}p^r(1-p)^{n-r}$

P(X=x) = P(total=x+10) What does this statement mean?

Many thanks

2. The total number of tosses MINUS 10 (for the 10 heads) will give you the number of tails observed.