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
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
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.