Let be two discrete random variables having finite moments (I assume this means ). Show that

a)if , then

b)if , then

HINT: You may consider the variable .

Again, with so much to do in so little time, I need help.

- Oct 15th 2010, 09:28 AMRuntyLet X,Y be two discrete random variables having finite moments
Let be two discrete random variables having finite moments (I assume this means ). Show that

**a)**if , then

**b)**if , then

HINT: You may consider the variable .

Again, with so much to do in so little time, I need help. - Oct 16th 2010, 07:01 AMCaptainBlack
It means something rather stronger than that, in fact far stronger than is needed here, all you need is that they have finite first moments.

Quote:

Show that

**a)**if , then

Quote:

**b)**if , then

HINT: You may consider the variable .

Again, with so much to do in so little time, I need help.

CB - Oct 16th 2010, 07:06 AMRunty
- Oct 16th 2010, 07:33 AMmatheagle
These are discrete, you have all the realization of X nonnegative and since probabilities are also nonnegative...

since

you are adding the product of two terms that cannot be negative. - Oct 16th 2010, 10:18 AMCaptainBlack
You can't do statistics without integration (rather you cannot do statistics using only discrete probability distributions other than in a half arsed manner), what I was trying to suggest is that the proof would be slightly more subtle if you were doing a course using measure theory.

CB - Oct 16th 2010, 10:21 AMRunty