Define the cumulative distribution function of Poisson distribution
The cumulative distribution function (CDF) of a Poisson distribution is a function that gives the probability that a random variable X, which follows a Poisson distribution with parameter λ, takes on a value less than or equal to a specific value x. It is denoted by F(x) and can be expressed as:
F(x) = P(X ≤ x) = ∑(k=0 to x) [(e^-λ * λ^k) / k!]
Where e is the base of the natural logarithm (approximately equal to 2.71828), λ is the rate parameter of the Poisson distribution, x is the specific value, and k is the value being summed over in the series.