binomial distribution

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binomial distribution

A student graphs a binomial distribution on the whiteboard.

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.
binomial distribution

A student graphs a binomial distribution on the whiteboard.

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

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