Question: The stochastic variable (X) is Poisson distributed with parameter (lambda=1). Find the distribution function (f) of (X), and calculate the expected value and standard deviation.

The stochastic variable $X$ is Poisson distributed with parameter $\lambda=1$. Find the distribution function $f$ of $X$, and calculate the expected value and standard deviation. What is $P(X \in\{0\})$ ?

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