The stochastic variable (X) is Poisson distributed with parameter (lambda=1). Find the distribution function (f) of (X),

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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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