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October 27th, 2017, 02:41 PM   #1
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Exclamation Prove that two variables follow a joint distribution

I'm really confused by this question (part a):



I know that the sum of normal random variables is also in itself a normal random variable. But how am I supposed to "show" that they are bivariate normal? Am I simply supposed start from the MGF of the bivariate normal distribution with the corresponding parameters, assume the RV's are independent, and then factor the MGF into the marginal MGFs? I'm pretty sure that doesn't prove anything, but that's about as far as I've managed to get with this question. I'm really just not sure what approach to take.
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October 27th, 2017, 03:03 PM   #2
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take a look at this,

particularly where they talk about $a_1,~a_2$

You can match what they describe exactly to the problem at hand.
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