IFoA April 2011 Q10 (ii)

[Chandrima]

Posting the question and solution of IFoA April 2011 Q10's part (ii). How is Var(Y) = 200*Var(X) + 200*E(X)2 coming? Can anybody please explain?? Do they mean E(x)^2 at the end of the expression? Even if they mean that how is it coming?? Please help.

 

[Varsha Agarwal]

V(S)=E(N)*V(X)+V(N)*E^2(X).
Square is written wrongly
Also in following steps it's 40^2 and 800^2.

 

[Chandrima]

V(S)=E(N)*V(X)+V(N)*E^2(X).
Square is written wrongly
Also in following steps it's 40^2 and 800^2.

Thanks a lot. Yes it was for compound distribution.

 

[Sam88]

How did they get Pr(Z<2000)=Pr(Y>9200)?