6.3 Flashcard Binomial and Geometric Distributions

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What is a binomial distribution?

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A binomial distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent states and is defined by two parameters: the number of trials (n) and the probability of success (p).

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What is a geometric distribution?

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A geometric distribution models the number of trials needed to get the first success in a series of independent Bernoulli trials, where each trial has two possible outcomes (success or failure) and the probability of success is constant.

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How do you calculate the mean of a binomial distribution?

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The mean (expected value) of a binomial distribution is calculated using the formula: E(X) = n * p, where n is the number of trials and p is the probability of success.

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How do you calculate the standard deviation of a binomial distribution?

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The standard deviation of a binomial distribution is calculated using the formula: SD = sqrt(n * p * (1 - p)), where n is the number of trials and p is the probability of success.

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What does it mean if a random variable follows a binomial distribution?

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It means that the random variable represents the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

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What does it mean if a random variable follows a geometric distribution?

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It means that the random variable represents the number of trials until the first success occurs in a series of independent Bernoulli trials.

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In a binomial distribution, what are the possible outcomes for each trial?

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The possible outcomes for each trial in a binomial distribution are 'success' or 'failure'.

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What is the significance of the parameter 'p' in a binomial distribution?

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The parameter 'p' represents the probability of success on each trial in a binomial distribution.

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What is the significance of the parameter 'n' in a binomial distribution?

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The parameter 'n' represents the number of independent trials conducted in a binomial distribution.

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How do you interpret the standard deviation in the context of a binomial distribution?

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The standard deviation indicates how much the number of successes in the trials is expected to vary from the mean.