garnentas3m

2022-01-16

What is the moment generating function of a Poisson distribution?

Becky Harrison

Expert

${e}^{\lambda \left({e}^{t}-1\right)}$
Explanation:
The moment generating function of a Poisson distribution is
${e}^{\lambda \left({e}^{t}-1\right)}$

Mary Nicholson

Expert

Let X be a discrete random variable with a Poisson distribution with parameter $\lambda$ for some $\lambda \in R>0$. Then the moment generating function MX of X is given by: $MX\left(t\right)={e}^{\lambda \left({e}^{t}-1\right)}$