Binomial probability distribution

Definition

A binomial probability distribution models the number of successes in a fixed number of independent trials, each with the same probability of success. It is defined by two parameters: the number of trials (n) and the probability of success (p).

5 Must Know Facts For Your Next Test

1. The binomial distribution formula is given by: $$P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$$ where $\binom{n}{k}$ is the combination formula.
2. The mean (expected value) of a binomial distribution is $\mu = np$.
3. The variance of a binomial distribution is $\sigma^2 = np(1-p)$.
4. A binomial experiment requires that each trial is independent and has only two possible outcomes: success or failure.
5. The sum of all probabilities in a binomial distribution equals 1.

Review Questions

Related terms

Combination:

A mathematical way to determine how many ways you can choose k items from n items without regard to order, denoted as $\binom{n}{k}$.

Bernoulli Trial:

A single experiment or trial that results in a success with probability p and failure with probability 1-p.

Discrete Random Variable:

A random variable that can take on only a finite or countably infinite set of values.