Define the cumulative distribution function of binomial
The cumulative distribution function (CDF) of a binomial distribution is a function that gives the probability that a random variable following a binomial distribution is less than or equal to a certain value. It is defined as the sum of the probabilities of all possible outcomes up to and including a given value.
For a binomial random variable X with parameters n (number of trials) and p (probability of success on each trial), the CDF F(x) is given by:
F(x) = P(X ≤ x) = ∑[k=0 to x] (n choose k) * p^k * (1-p)^(n-k)
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes out of n trials.