The moment generating function of a poisson random variable X is given as $M_x(t)=e^{5e^t-5}$. Calculate $P(X \neq 5)$

I can only think of using mgf to do expected value.....

  • $\begingroup$ Can you compute P(X=5)? $\endgroup$ – Did Dec 13 '13 at 9:32
  • $\begingroup$ so I just solve the normal poisson random variable 1-P(X=5)? i got confused with the moment generating function... $\endgroup$ – natsu Dec 13 '13 at 9:33
  • $\begingroup$ ok got it so the point of this question is to realize the lambda... thanks! $\endgroup$ – natsu Dec 13 '13 at 9:35
  • 1
    $\begingroup$ The MGF allows to compute the parameter, which one needs to know P(X=5). $\endgroup$ – Did Dec 13 '13 at 9:36

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