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Math Help - Mean of a poisson random variable

  1. #1
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    Mean of a poisson random variable

    Please refer to attached image

    How is it that the k term from the second line disappears, and then in the third line everything is multiplied by aλ ?
    Also the power change from k to (k-1), as does the factorial.

    I cannot see the reason for this
    Attached Thumbnails Attached Thumbnails Mean of a poisson random variable-mean-poisson.jpg  
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  2. #2
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    Re: Mean of a poisson random variable

    For step 2, notice that when k = 0 then anything times that is 0 - so basically you have 0*blah + Sigma(k=1,infinity) = Sigma(k=1,infinity) blah.

    For step 3 we note that k! = k*(k-1)! (property of factorials) and that a^(b+1) = a*a^b. Re-arrange those for the results in this step.

    Last step uses the fact that the sum of all probabilities is equal to 1.
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  3. #3
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    Re: Mean of a poisson random variable

    oh of course! thanks chiro
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