Unlock the power of probability with our Negative Binomial Distribution Calculator. Easily determine the likelihood of observing a specific number of failures before successes in a series of independent Bernoulli trials. Perfect for students, statisticians, and researchers modeling discrete events.
Formula:
The probability mass function for the Negative Binomial Distribution, where X represents the number of failures before the r-th success, is given by:
P(X=k) = C(k + r - 1, k) × pr × (1 - p)k
- P(X=k): The probability of exactly
kfailures before ther-th success occurs. - C(n, k): The binomial coefficient "n choose k", calculated as
n! / (k! × (n-k)!). - k: The number of observed failures.
- r: The number of required successes.
- p: The probability of success on a single trial (0 ≤ p ≤ 1).