(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let X and Y be independent and normal, then we know that

It must be the case that X+Y and X are jointly normal

Therefore we can apply the projection theorem:

which states that if A and B are jointly normal then VAR(A|B)=VAR(B)-[tex]\rho[/tex]^2VAR(B) , apply the theorem to A=X+Y, B=Y to find

VAR(X+Y|X)

There is a similar procedure of finding E(X+Y|X)

I know how to do the above. However, what I don't know is what if X and Y are independent but each are UNIFORMLY distributed on [-1,1]

What is:

1.VAR(X+Y|X)

2.E(X+Y|X)

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Sum of independent uniform distribution conditional on uniform

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