CT3 IFoA October 2012 Question 4

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.

 

Hi John,

Could you please elaborate on that? So is my method right/wrong? If wrong why so?

 

Yeah that is what I got too.

Thank you for replying