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Aggregate model

  1. May 6, 2014 #1
    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)??
     
  2. jcsd
  3. May 9, 2014 #2

    Stephen Tashi

    User Avatar
    Science Advisor

    Let's make the question more readable. (See post #3 in the thread https://www.physicsforums.com/showthread.php?t=617567)

    Is it this?:

     
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