Question: Can you please help with the following homework problem. Please show full work, thank you. Problem 3. (15 pts.) Let X1 and X2 be two

Can you please help with the following homework problem. Please show full work, thank you.

Problem 3. (15 pts.) Let X1 and X2 be two random variables constituting a random sample from Normal(0, 1/5). A bivariate vector (Z, W) is defined as follows: Z = 2X1 + X2 and W = X1 - 2X2. 1. Find the marginal distributions of Z and W. 2. Show that Z and W are independent. 3. Find the distribution of Z2 + W2

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