If a random variable X follows a Poisson distribution with mean λ=4, find P(X=0).

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Substitute $r=0$ into the Poisson probability formula; $0!=1$ and $\lambda^0=1$ , so only the $e^{-\lambda}$ factor survives.

$P(X=r)=e^{-\lambda}\dfrac{\lambda^r}{r!}$ …

Q.If a random variable XXX follows a Poisson distribution with mean λ=4\lambda=4λ=4, find P(X=0)P(X=0)P(X=0).