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Let X1 and X2 be uniformly distributed in the region [−1,1]×[0,1]∪(1,2]×(1,3]. 1. Find Joint and Marginal...

Let X1 and X2 be uniformly distributed in the region [−1,1]×[0,1]∪(1,2]×(1,3].

1. Find Joint and Marginal pdf of X1 and X2.

2.Find V (X1 + 3X2) ，( I‘ve asked this question already, but the person didn't give me the correct answer, so please, dont waste my question, if you dont know how to answer this question.)

Expert Solution

Given and are uniformly distributed in the region .

The region is same as

1) Since the joint pdf is uniform we have

.

The condition for pdf is

Thus the joint pdf is

The marginal pdfs are

2) The expected values are

The second order moments are

The variance since and are independent is

orchestra answered 2 years ago

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