How Can You Calculate the Expected Value E(X^2(3Y-1))?

[adamwitt]

Expected Values... E(X^2(3Y-1))

Homework Statement

What is the Expected Value of E(X²(3Y-1))

Homework Equations

Properties of Expected Values.
E(X+c) = E(X) + c
E(X+Y) = E(X) + E(Y)

The Attempt at a Solution

I tried googling for a few of the properties I could use but I'm not sure which ones to use, or maybe I haven't found the required property?
I have been given the data and worked out the marginal probability mass functions so I can work out E(X), E(Y), and E(XY)

But I was wondering if I could decompose the problem quickly using properties of expected values, instead of having to do all the math involved manually calculating the expected value?
If so, which properties should I take a look at in order to achieve this? Thanks!

 

[adamwitt]

Ok I gave it a crack using basic expansion, lemmy know if I am close :)

E(X²(3Y-1))
E(3X²Y-X²)
3E(X²Y)-E(X²)

Then from there its a fairly simple process of taking the integrals of the various functions. In my examples case the marginal prob dens functions are only defined for certain values so all I got to do is E = 3sum(X².y(x)) - sum(X².y(x))and badabing.

Yay or nay? :D

 

[Ray Vickson]

Homework Statement

What is the Expected Value of E(X²(3Y-1))

Homework Equations

Properties of Expected Values.
E(X+c) = E(X) + c
E(X+Y) = E(X) + E(Y)

The Attempt at a Solution

I tried googling for a few of the properties I could use but I'm not sure which ones to use, or maybe I haven't found the required property?
I have been given the data and worked out the marginal probability mass functions so I can work out E(X), E(Y), and E(XY)

But I was wondering if I could decompose the problem quickly using properties of expected values, instead of having to do all the math involved manually calculating the expected value?
If so, which properties should I take a look at in order to achieve this? Thanks!

You need to work out E(X^2*Y). If X and Y are independent, this would be E(X^2)*E(Y), but it they are correlated, there is no simple expression. By the way, you say you have worked out the marginal probability mass functions so can work out E(XY). This statement (the "so can ..." part) is false if X and Y are not independent (or, at least, uncorrelated), because in that case you need the full bivariate probability mass function f(x,y) in order to work out E(XY).

RGV