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Binomial Distribution definitions

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  • Binomial Experiment
    A process with two possible outcomes per trial, repeated a fixed number of times, where each trial is independent.
  • Success
    A desired outcome in a binomial experiment, such as landing heads in a coin flip or pulling a red marble.
  • Failure
    The alternative outcome to success in a binomial experiment, like tails in a coin flip or pulling a blue marble.
  • Trial
    A single repetition of a binomial experiment, such as one coin flip or one marble draw.
  • Probability of Success
    The likelihood of achieving the desired outcome in a single trial, denoted by p.
  • Probability of Failure
    The likelihood of not achieving the desired outcome in a single trial, calculated as 1 minus p and denoted by q.
  • Discrete Random Variable
    A variable representing countable outcomes, such as the number of successes in a binomial experiment.
  • Number of Trials
    The total count of independent repetitions in a binomial experiment, denoted by n.
  • Expected Value
    The average number of successes anticipated in a binomial experiment, found by multiplying n and p.
  • Standard Deviation
    A measure of variability in the number of successes, calculated as the square root of n times p times q.
  • Variance
    The squared value of the standard deviation, representing the spread of possible outcomes in a binomial experiment.
  • Complement
    The probability of the opposite event, used to simplify calculations for ranges of outcomes.
  • Combination
    A count of possible ways to arrange a specific number of successes among trials, often written as n choose x.
  • Binomial Probability Formula
    An equation combining combinations, probabilities of success and failure, to find the chance of a specific number of successes.
  • Cumulative Probability
    The total probability of achieving up to a certain number of successes, often calculated using binom CDF.