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

Printable View

- September 15th 2013, 10:47 PM99.95Mean 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 a**λ**?

Also the power change from k to (k-1), as does the factorial.

I cannot see the reason for this - September 16th 2013, 02:49 AMchiroRe: 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. - September 16th 2013, 04:29 AM99.95Re: Mean of a poisson random variable
oh of course! thanks chiro