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Dec 17, 20241 min read

Multiple RVs

In the two variable case, we have:

Z = g (X, Y)

The CDF of $Z$ is found by finding the equivalent event of $Z \leq z$ .

If $X, Y$ are independent, then the PDF of $Z$ is given by the convolution:

f_{Z} (z) = \int_{- \infty}^{\infty} f_{X} (x^{'}) f_{Y} (z - x^{'}) d x^{'}