- #1
johnnytzf
- 3
- 0
consider the following model for aggregate claim amounts S:
S=X1+X2+...+XN
where the Xi are independent, identically distributed random
variables representing individual claim amounts and N is a random
variable,independent of the Xi and representing the number of
claims.let X has ìx and let N has mean ìN and variance ó²N.
a) show that E(SN)=ìX ( ì²N + ó²N ) by considering expected values
conditional on the value of N
b) hence derive an expression for the covariance between S and N.
I know that
E(S) = E(E(S|N)) = E(N)E(S) = ìXìN,
Var(E(S|N)) = Var(N)Var(S) = ó²Xó²N
but how to link it with E(SN)??
S=X1+X2+...+XN
where the Xi are independent, identically distributed random
variables representing individual claim amounts and N is a random
variable,independent of the Xi and representing the number of
claims.let X has ìx and let N has mean ìN and variance ó²N.
a) show that E(SN)=ìX ( ì²N + ó²N ) by considering expected values
conditional on the value of N
b) hence derive an expression for the covariance between S and N.
I know that
E(S) = E(E(S|N)) = E(N)E(S) = ìXìN,
Var(E(S|N)) = Var(N)Var(S) = ó²Xó²N
but how to link it with E(SN)??