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IFoA April 2009 Q10 (iii)

C

Chandrima

Member
Can anyone check the solution of (iii)'s last part? Why are they taking V(S)=V(N).E(Y^2) = 500*E(Y^2) = 500*24398.3967?? Should not it be V(S) = (E(Y))^2.V(N)+E(N).V(Y)? I have understood the entire question just stuck at the end. Can anybody quickly confirm whether the last line of the solution is wrong or not?
 
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This is the alternative (and equivalent) formula for the variance of a compound Poisson.
This formula is given in the notes Chapter 7 Section 3.4 and in the formula book on page 16.
 
Thank you sir! I was thinking even by using the generalized formula of V(S) = [E(Y)]^2*V(N)+V(Y)*E(N), I should have got the same answer as given in the solution, and hence asked this question. Later I discovered, while finding out E(Y^2), I mistakenly used the value of V(X) and E(X^2) and hence my answer did not match. I have rectified it then.
 
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