# Transforming

Let X1, X2, X3 be iid with common pdf f(x)= e^(-x), x>0, 0 elsewhere. Find the joint pdf of Y1=X1/X2, Y2=X3/(X1+X2), and Y3= X1+X2. Are Y1, Y2, Y3 mutually independent? Please show detail on boundaries of the transformation.

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#### Solution Preview

Solution. Since X1, X2, X3 be iid with common pdf f(x)= e^(-x), x>0, 0 elsewhere, we have the joint pdf is

See attached

So, we can compute the Jocobian of the above transformation as follows.

See attached

Let X1, X2, X3 be iid with common pdf f(x)= e^(-x), x>0, 0 elsewhere. Find the joint pdf of Y1=X1/X2, Y2=X3/(X1+X2), and Y3= X1+X2. Are Y1, Y2, Y3 mutually independent? Please show detail on boundaries of ...

#### Solution Summary

This solution describes how to find the joint pdf os Y1=X1/X2 and two other equations. The solution computes the Jocobian of the above information to determine the joint pdf of Y_1, Y_2, Y_3.