Proofs in Exams

I wonder if someone can tell me the difference between the terms "prove" and "prove from first principals" - also which formulas you can simply quote. For example, in CT3 Question 6.29, it asks to prove that the sum of 2 Chi-square rvs with m and n degrees of freedom relates to a chi-square m+n rv. I proved by multiplying the 2 MGFs together. However in the answers, they used the MGF formula MX(t)=E(exp(tX)) - not that that makes it too more onerous but obviously I don't want to waste time taking longer to prove something than necessary - would I have got 100% for my approach in an exam do you think?

Thanks.

Stewart.

 

So would my proof below for Que 2.3 have been acceptable do you think?

 

In the exam, you probably would have to prove that multiplying the MGF's together would work in the first place. There's usually a factor you have to pull out of the exponentials, giving rise to the MGF for that distribution.

I'd take the answers in the QA bank as model answers for the exam.

 

Hmmm thats a good point - thanks all.

 

It seems an odd thing to be asked to prove. A chi^2(m) distribution is the sum of m squared standard normal variates, and so by definition the sum of two chi^2 variates is distributed on m+n degrees of freedom.

 

As this thread is already titled proofs:

Can I check whether the proof of a Poisson process is a requirement?

 

There was a really good previous thread on this type of thing:

Here

Hope it helps!

Tim