Binomial distribution

The probability distribution of the number of successes in a fixed number of independent trials, each with the same probability of success.

Bernoulli trial: A random experiment with two outcomes, conventionally called success and failure. Each trial in a binomial experiment is a Bernoulli trial.
Independent and identically distributed random variables: Random variables that are mutually independent and share the same probability distribution. The trial outcomes satisfy independence and have a common success probability.
Coin flipping: A random experiment in which a coin lands on one of its faces. Counting heads in a fixed number of independent flips is a standard binomial model.
Poisson binomial distribution: The distribution of the number of successes in independent Bernoulli trials with differing success probabilities. It relaxes the equal-success-probability assumption.
Variance: A measure of the average squared deviation of a random variable from its mean. Its value is the trial count times the success probability times the failure probability.
Probability mass function: A function assigning probabilities to the possible values of a discrete random variable. It gives the probability of every possible success count.
Random variable: A function that assigns a numerical value to each outcome of a random experiment. The binomial variable records the number of successes.
Quality control: Methods for monitoring and improving whether products or processes meet specifications. A production batch can be modeled by counting defective items when defect chances are stable and independent.
Hypergeometric distribution: The distribution of successes in a fixed-size sample drawn without replacement from a finite population. Sampling without replacement makes outcomes dependent, unlike the binomial model.
Central limit theorem: A theorem stating conditions under which standardized sums of random variables approach a normal distribution. It explains why large-count binomial distributions can be approximated by a normal curve.

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