Definition

1. Noun:
   • A theoretical probability distribution: The binomial distribution is a discrete probability distribution. It models the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant for every trial.

Usage Examples

• Noun:
  • The probability of getting exactly three heads in five coin flips can be calculated using the binomial distribution.
  • In quality control, the binomial distribution is often used to model the number of defective items in a random sample.
  • To apply the binomial distribution, you must ensure the trials are independent and the probability of success does not change.

Advanced Usage

• "To follow a binomial distribution": To have its probabilities described by this specific model.
  • If a process meets the required assumptions, the number of successes can be said to follow a binomial distribution.
• "Parameters of the binomial distribution": The two values that define a specific binomial distribution: the number of trials (n) and the probability of success in each trial (p).
  • The shape of the binomial distribution is determined by its parameters, n and p.

Variants and Related Words

• Binomial (adj): Relating to or consisting of two terms; having two names. In statistics, it specifically refers to the two-outcome nature of each trial.
  • The experiment has a binomial outcome: pass or fail.
• Bernoulli trial (n): A single random experiment with exactly two possible outcomes. A binomial distribution is the sum of outcomes from a sequence of independent Bernoulli trials.
  • Each flip of the coin is a Bernoulli trial with a probability of heads equal to 0.5.

Synonyms

• Bernoulli distribution: This is a specific case of the binomial distribution where the number of trials, n, is equal to 1.

Related Phrases and Concepts

• Binomial probability formula: The mathematical formula used to calculate probabilities for a binomial distribution.
  • You need to use the binomial probability formula to find the exact chance of that event.
• Binomial experiment: An experiment that satisfies all the conditions for using the binomial distribution (fixed n, independence, constant p, two outcomes).
  • Surveying 100 people for a yes/no question is a classic binomial experiment.

Noun

1. a theoretical distribution of the number of successes in a finite set of independent trials with a constant probability of success