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Glen_b
Glen_b
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I came across a problem where the marginal distribution of a random variable Y$Y$, f(y) = c/y^2$f(y) = c/y^2$ and f(X|Y) = 1/y$f(x|y) = 1/y$. 

Can iI simply multiply these two to get f(XY)$f(x,y)$ the joint distribution of X$X$ and Y$Y$, which in this case will be c/y^3$c/y^3$. And then integrate it over all Y$Y$ to find the marginal distribution of X$X$.

I came across a problem where the marginal distribution of a random variable Y, f(y) = c/y^2 and f(X|Y) = 1/y. Can i simply multiply these two to get f(XY) the joint distribution of X and Y, which in this case will be c/y^3. And then integrate it over all Y to find the marginal distribution of X.

I came across a problem where the marginal distribution of a random variable $Y$, $f(y) = c/y^2$ and $f(x|y) = 1/y$. 

Can I simply multiply these two to get $f(x,y)$ the joint distribution of $X$ and $Y$, which in this case will be $c/y^3$. And then integrate it over all $Y$ to find the marginal distribution of $X$.

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statBeginner
statBeginner
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Marginal Distribution from Conditional Distribution

I came across a problem where the marginal distribution of a random variable Y, f(y) = c/y^2 and f(X|Y) = 1/y. Can i simply multiply these two to get f(XY) the joint distribution of X and Y, which in this case will be c/y^3. And then integrate it over all Y to find the marginal distribution of X.