Moment Generating Function (Poisson Distribution) Watch

username2110335
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I understand how the exponential function is used to get the 3rd part of the answer which is e-leele^t

Could someone please explain what happens to take the e-l out of the sum and show how the etl can be put inside the brackets?
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Gregorius
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(Original post by JKITFC)
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I understand how the exponential function is used to get the 3rd part of the answer which is e-leele^t

Could someone please explain what happens to take the e-l out of the sum and show how the etl can be put inside the brackets?
As far as the sum is concerned, the e^{-\lambda} is a constant and can therefore be taken outside of the sum. For the second question,

\displaystyle e^{-\lambda} e^{\lambda e^t} = e^{ -\lambda + \lambda e^t} = e^{\lambda (e^t - 1)}
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