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Help!! Exam P question!!

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  • Help!! Exam P question!!

    I have a question about P/1 exam, i hope someone can give me a clue, thanks!!
    That is one of the example in Actex P/1 exam study manual, example 10-3 p. 239.

    The probability of a claim amount given a claim occurs is given, qi, and the mean and variance of the conditional distribution of claim amount given a claim occurs is given, E[ Bi ], Var [ Bi ]. When the loss random variable is given in this form, we have for policy i, E[ Xi ] = qi*E [Bi], and Var [Xi] = qi*(1-qi)*(E[Bi])^2 + qi*Var[Bi]

    My question is how the equation Var[Xi] comes from?? Can someone can explain to me?? Thanks for all your help, your advise is very important to me!!



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