\(Y\) is a random variable that can take any positive integer value. The likelihood of these outcomes is given by the Poisson pdf

\[p(y)=\frac{\lambda^{y}}{y!} \exp \{-\lambda\}\]

By using the fact that, for a discrete random variable, the pdf gives the probabilities of the individual events occurring and that probabilities are additive,

(a) compute the probability that \(Y \leq 4\) for \(\lambda=5\), i.e. \(P(Y \leq 4)\).

(b) Using the result of (a) and the fact that one outcome has to happen, compute the probability that \(Y>4\). (one of the two events, \(Y \leq 4\) and \(Y>4\), has to happen.)