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CT3 IFoA October 2012 Question 4

T

trackr

Member
Hi there, I understand that they used convolutions for this question.

However when I solved it without seeing the answer, I used MGFs. Would I get full marks for that method?

I assumed U to be continuous uniform dist. So Mz(t)=E (exp(t^z)) = E (exp(t^(U+X))).

Now since U & X are independent. I separated them out and simplified it. In the end I got the distribution of Z as Uniform dist with a = t/2 and b = (2+t)/2.

Can someone reject or confirm my method?

Thanks in advance!
 
Range of Z is from -∞ to +∞. So it can't be a Uniform Distribution.
 
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