Originally Posted by

**dokrbb** Hi,

So I have a problem given as example in class, but with a whole bunch of steps skipped (don't know if intentionally...):

For two RVs, $X_1, X_2$, the joint pmf is given by:

$p(m, n) = {{n}\choose{m}}p_1(1-p_1)^{n}p_2^{m}(1-p_2)^{n-m}$

Now, marginal distrib. of $X_1$ is defined as:

$p_{X_1}(m) = \sum_{\text{all } n} p(m,n) = \sum_{n = m}^{\infty}{{n}\choose{m}}p_1(1-p_1)^{n}p_2^{m}(1-p_2)^{n-m} = $

$ p_1p_2^{m}(1-p_1)^{m} \sum_{n = m}^{\infty}{{n}\choose{m}}(1-p_1)^{n-m}(1-p_2)^{n-m} = $