Suppose and are both integer-valued random variables. Let

Show that

Solution

Consider

So

as

So

So our result is proven

- December 5th 2011, 06:25 PMI-ThinkConditional probability of integer-valued random variables: (solution checking)
Suppose and are both integer-valued random variables. Let

Show that

Solution

Consider

So

as

So

So our result is proven

- December 6th 2011, 11:47 AMMooRe: Conditional probability of integer-valued random variables: (solution checking)
Hello,

I corrected some LaTeX errors and a typo in the way you defined q (it's the conditional probability, not the joint probability as you initially wrote). And your solution is perfect :p