Bivariate transformation method


Assume that Y1 and Y2 are independent exponentials with mean beta=1. Illustrate the following two functions of Y1 and Y2 : U1 = g1(Y1,Y2)= Y1 and U2= g2(Y1,Y2)=2Y1 + 3Y2. Employ the bivariate transformation method to find the joint pdf fU1U2(u1,u2) of U1 and U2 for all points (u1,u2) in the support B. Do it in the following order:

1) Find the inverse functions.

2) Find and sketch the support B.

3) Find the Jacobian of the inverse functions.

4) Find fU1U2(u1,u2), simplified as much as possible.

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Basic Statistics: Bivariate transformation method
Reference No:- TGS0872804

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