If $E(X) \sim \mathsf{Poisson}(\lambda),$ what is
a) $P(X=2)$
b) $P(X>2)$
c) $P(X^2>2)$
I don't understand what this is trying to say and I don't see how I calculate the Poisson when I'm only given that information. Please help!
2026-03-30 18:05:24.1774893924
Help with poisson distribution confused / lack information
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By definition, a random variable $X \sim \text{Poisson}(\lambda)$ has pmf \begin{equation*} f_X(x)=P(X=x)=e^{-\lambda}\frac{\lambda^x}{x!}, \text{ where } x \in \{0,1,\dots\} \end{equation*} If you are not given a specific value for $\lambda$, you answers will just be in terms of $\lambda$. Can you answer your questions now?