# Homework Help: Interpretation of random variable

1. Sep 22, 2009

### Obraz35

1. The problem statement, all variables and given/known data
The probability mass function of a random variable X is:
P(X=k) = (r+k-1 C r-1)pr(1-p)k
Give an interpretation of X.

2. Relevant equations

3. The attempt at a solution
The PMF looks like the setup for a binomial random variable. The first combination looks like you are arranging r-1 successes in r+k-1 slots. And the pr seems like it is giving the probability of r successes occurring. But I don't see what X as a whole is standing for.

2. Sep 23, 2009

### lanedance

i think you;re almost there, so i assume you mean
$$P(X=k) = C_{r-1}^{r+k-1}p^r(1-p)^k$$

can re-write this as
$$P(X=k) = p.C_{(r-1)}^{k+(r-1)}p^{r-1}(1-p)^{k}$$

which as you say comparing with the binomial distribution is for n trials, m success, and probabilty of success of p

can re-write this as
$$P(M=m) = p.C_{m}^{n}p^{n-m}(1-p)^{m}$$

so your distribution is effectively p (the probabilty of a single success) times the probability of r-1 successes out of r-1+k trials (with probability of success p).

any ideas for an interpretation of this as a total entity?