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Assume that X~N(0, 1), Y~N(0, 1) and X and Y are independent variables. Let Z =...

Assume that X~N(0, 1), Y~N(0, 1) and X and Y are independent variables.

Let Z = X+Y, and joint density of Y and Z is expressed as f(y, z) = g(z|y)*h(y)

g(z|y) is conditional distribution of Z given y, and h(y) is density of Y

how can i get f(y, z)?

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Answer #1

without using g(z|y) you can directly find f(y,z) in the following way

The transformation formula which I have used here, you can find it in any statistics book( chapter: transformations of random variables) Thank you.

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