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The Poisson distribution is a probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space, given that these events occur with a known constant mean rate and independently of the time since the last event. It is particularly useful for modeling rare events.

In the context of the Poisson distribution, the parameter μ (mu) represents the average number of events in the specified interval. It is a crucial component for calculating probabilities, as it defines the shape and scale of the distribution. For example, if μ = 6, it indicates that, on average, 6 events are expected to occur.

The Probability Mass Function (PMF) of a discrete random variable gives the probability that the variable is equal to a specific value. For the Poisson distribution, the PMF is calculated using the formula P(X = k) = (e^(-μ) * μ^k) / k!, where k is the number of events, e is Euler's number, and k! is the factorial of k. This formula allows us to find the probability of observing exactly k events.