Our free Binomial Cumulative Distribution Function (CDF) Calculator helps you quickly find the cumulative probability of 'at most k' successes in a series of 'n' independent Bernoulli trials. Input your number of trials, successes, and success probability to get instant results for P(X ≤ k).
Formula:
The Binomial Cumulative Distribution Function (CDF) calculates the probability of getting at most 'k' successes in 'n' independent trials, where each trial has a probability of success 'p'.
The formula is a summation of individual Binomial Probability Mass Function (PMF) values:
P(X ≤ k) = ∑i=0k C(n, i) * pi * (1 - p)n-i
- P(X ≤ k): The cumulative probability of at most 'k' successes.
- n: The total number of trials.
- k: The number of successes (at most this value).
- p: The probability of success on any single trial (between 0 and 1).
- C(n, i): The number of combinations of 'n' items taken 'i' at a time, calculated as n! / (i! * (n-i)!).