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# Probability question Watch

1. Hi, I have a couple of questions.

If you know the probability mass function of X and Y and then work out conditional mass function of XlY and YlX, how do you work out: E(Y-XlX<Y)?
What im thinking is writing out all the values of y transformed to y-x and only considering x<y then doing the mean of this data. is this right?

also, does anyone know about moment generating functions? i know that M_X=E(e^(tx)) but what does this do? why do we want to know M_X?

thanks!!
2. (Original post by number23)
Hi, I have a couple of questions.

If you know the probability mass function of X and Y and then work out conditional mass function of XlY and YlX, how do you work out: E(Y-XlX<Y)?
What im thinking is writing out all the values of y transformed to y-x and only considering x<y then doing the mean of this data. is this right?
Depending on the amount of pmf's it's a fair bit of work, but yes, your methodology would work. Assuming you meant all the values of y transformed by all the values of x.

Notice that X<Y can be rewritten Y-X > 0.

So if you restrict your calculations to just those combinations satisfying that criterion it will more than halve your working.

also, does anyone know about moment generating functions? i know that M_X=E(e^(tx)) but what does this do? why do we want to know M_X?

thanks!!
Not something I've studied, unfortunately.
3. (Original post by ghostwalker)
Depending on the amount of pmf's it's a fair bit of work, but yes, your methodology would work. Assuming you meant all the values of y transformed by all the values of x.

Notice that X<Y can be rewritten Y-X > 0.

So if you restrict your calculations to just those combinations satisfying that criterion it will more than halve your working.

Not something I've studied, unfortunately.
great thanks, i was wondering if there was a specific formula i needed to remember. so say if x could be: 1 or 2. y: could be 1 or 2. then y-x can be: 0, -1, 1, 0
but we just consider: 0, 1, 0 hence e(x)=1/3 ??
thanks
4. (Original post by number23)
great thanks, i was wondering if there was a specific formula i needed to remember. so say if x could be: 1 or 2. y: could be 1 or 2. then y-x can be: 0, -1, 1, 0
but we just consider: 0, 1, 0 hence e(x)=1/3 ??
thanks
Well it's a strict inequality so we are only interested in one of those 4 combinations.
5. (Original post by ghostwalker)
Well it's a strict inequality so we are only interested in one of those 4 combinations.
so is 1/3 not correct?
6. (Original post by number23)
also, does anyone know about moment generating functions? i know that M_X=E(e^(tx)) but what does this do? why do we want to know M_X?

thanks!!

A nice idea, I think.
7. (Original post by number23)
so is 1/3 not correct?
Nope. There is only one combination that satisfies Y>X.
8. (Original post by number23)
also, does anyone know about moment generating functions? i know that M_X=E(e^(tx)) but what does this do? why do we want to know M_X?
Well, differentiating M_X n times w.r.t. t and setting t = 0 will give you the n-th moment (hence the name).

Another very useful property is that if X and Y are independent, then .

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