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Poisson Distribution homework

  1. Feb 17, 2009 #1
    1. The problem statement, all variables and given/known data
    An actuary has discovered that policyholders are three times as likely to file two claims as to file four claims. If the number of claims filed has a Poisson distribution, what is the variance of the number of claims filed?


    2. Relevant equations[/]
    P(x)=e^(-lamda)*(lamda^x)/x! Var(x)=lamda


    3. The attempt at a solution
    I know that P(2)=3P(4) and that P(2)=e^(-lamda)*(lamda^2)/2 and that P(4)=e^(-lamda)*(lamda^4)/4! So I set these equal to find lamda and that is the variance. The solution given to me is P(2)=e^(lamda)*(lamda^2)/2=3*e^(-lamda)*(lamda^4)/4!=3*P(4)*24*lamda^2=6*lamda^4 I don't understand the last two equalities. Any help? where do the 24*lamda^2 comefrom and how do they get 6*lamda^4?
    Thanks
     
  2. jcsd
  3. Feb 19, 2009 #2
    Is this a typo? if so how would I go about solving the problem using the method I've started? or any other way?
    Thanks
     
  4. Feb 19, 2009 #3

    Mark44

    Staff: Mentor

    From the given information,
    [tex]P(2) = \frac{e^{-\lambda}\lambda^2}{2!} = 3P(4) = 3\frac{e^{-\lambda}\lambda^4}{4!} [/tex]
    From this, we get
    [tex]\frac{e^{-\lambda}\lambda^2}{2} = 3\frac{e^{-\lambda}\lambda^4}{24}[/tex]
    so
    [tex]\frac{e^{-\lambda}\lambda^2}{2} = \frac{e^{-\lambda}\lambda^4}{8}[/tex]
    or
    [tex]4e^{-\lambda}\lambda^2} = e^{-\lambda}\lambda^4}[/tex]
    That works out to [itex]4\lambda^2 = \lambda^4[/itex]
    Can you take it from there?

    BTW, the name of this Greek letter is lambda.
     
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