Question
Let [mathjaxinline](X,Y)[/mathjaxinline] be a pair of random variables with joint density [mathjaxinline]h(x,y) = x+y[/mathjaxinline] over the space [mathjaxinline][0,1]^2[/mathjaxinline].
What is the marginal density of [mathjaxinline]X[/mathjaxinline]? We denote this by writing [mathjaxinline]h(x)[/mathjaxinline].
[mathjaxinline]h(x)=[/mathjaxinline]
What is the conditional density of [mathjaxinline]Y[/mathjaxinline] given [mathjaxinline]X=x[/mathjaxinline]? We denote this by writing [mathjaxinline]h(y|x)[/mathjaxinline].
[mathjaxinline]h(y|x)=[/mathjaxinline]
Consider the joint density setup as in the previous problem. What is the variance of Y given X=x?
\textsf{Var}(Y | X=x)=
What is the marginal density of [mathjaxinline]X[/mathjaxinline]? We denote this by writing [mathjaxinline]h(x)[/mathjaxinline].
[mathjaxinline]h(x)=[/mathjaxinline]
What is the conditional density of [mathjaxinline]Y[/mathjaxinline] given [mathjaxinline]X=x[/mathjaxinline]? We denote this by writing [mathjaxinline]h(y|x)[/mathjaxinline].
[mathjaxinline]h(y|x)=[/mathjaxinline]
Consider the joint density setup as in the previous problem. What is the variance of Y given X=x?
\textsf{Var}(Y | X=x)=
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