What is the formula for the Binomial Distribution?

The formula for the Binomial Distribution is correctly stated as p(x) = n!/[(n-x)! * x!]p^x(1-p)^(n-x). This formula is used to determine the probability of obtaining exactly x successes in n independent Bernoulli trials, each with a probability of success p.

In this context, n represents the total number of trials, x is the number of successes we are interested in, and p is the probability of success in a single trial. The term n! represents the factorial of n, which calculates the number of ways to arrange n items. The divisors (n-x)! and x! account for the arrangements of the failures and successes, respectively. The term p^x captures the probability of achieving x successes, while (1-p)^(n-x) corresponds to the probability of having (n-x) failures.

This makes the choice representative of the fundamental characteristics of the Binomial Distribution, which models a discrete random variable representing the number of successes in a fixed number of trials.

The other options presented do not pertain to the Binomial Distribution. One option describes the Poisson Distribution, which is relevant to events occurring over a fixed interval, while another involves the calculation of correlation