Lecture1.TransformationofRandomVariables
1. The joint density of two random variables X 1 and X 2 is f(x 1,x 2)=2e−x 1e−x 2, where 0 <x 1 <x 2 <∞;f(x 1,x 2) = 0 elsewhere. Consider the transformation Y 1 =2X 1,Y 2 = X 2 −X 1. Find the joint density of Y 1 and Y 2,and conclude thatY 1 and Y 2 are independent. 2. Repeat Problem 1 with the following new data. The joint density is ...
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