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Binomial Distribution definitions

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  • Binomial Experiment
    A process with a fixed number of independent trials, each resulting in one of two possible outcomes.
  • Success
    A desired outcome in a trial, such as getting heads in a coin flip or a red marble from a bag.
  • Failure
    An outcome that is not the desired one, like tails in a coin flip or a blue marble from a bag.
  • Trial
    A single repetition of an experiment, such as one coin flip or one marble draw.
  • Independence
    A property where the outcome of one trial does not affect the outcome of another.
  • Probability of Success
    The likelihood, denoted as p, that a single trial results in a desired outcome.
  • Probability of Failure
    The likelihood, denoted as q, that a single trial does not result in a desired outcome; calculated as 1 minus p.
  • Number of Trials
    The total count of times an experiment is repeated, represented by n.
  • Number of Successes
    The count of times the desired outcome occurs in all trials, represented by x.
  • Expected Value
    The average number of successes anticipated, found by multiplying the number of trials by the probability of success.
  • Standard Deviation
    A measure of spread in the number of successes, calculated as the square root of n times p times q.
  • Variance
    A measure of dispersion in the number of successes, equal to n times p times q.
  • Combination
    A count of ways to arrange a specific number of successes among trials, often written as n choose x.
  • Complement
    The set of outcomes not included in the event of interest, used to simplify probability calculations.
  • Binom PDF
    A calculator function that finds the probability of exactly a certain number of successes in a binomial experiment.
  • Binom CDF
    A calculator function that finds the probability of at most a certain number of successes in a binomial experiment.