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Help with total expectation formula

  1. Jul 29, 2008 #1
    I need some help with "law of total expectation".

    Sorry for my English, I don't know the right English expressions.

    The Problem is:
    People come (show in) with with Poisson rate of 10 people per hour.
    There is a 0.2 chance that a person will give money to a beggar sitting in the corner.
    The time that beggar is sitting is U[3,8] (continuous) hours.

    Need to find the expectation E of people that will give money.

    I mark:
    N(t)~P(10*0.2*t) as the number of people giving money per hour.
    X~U(3,8) time that beggar is sitting.

    The given solution is following : E(N(X))=E(E(N(X)|X))=E(2X)=2*(3+8)/2

    What I don't understand is their usage law of total expectation, according to the formula it should be like this:

    E(Y)=E[E[Y|X]]=[tex]\int[/tex]E[Y|X=x]*[tex]f_{x}[/tex](x)dx

    And this is not what they have.....
     
  2. jcsd
  3. Aug 1, 2008 #2
    Well, anyone?
     
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