Binomial vs Geometric Distributions

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What is a Binomial Distribution?

Back

A Binomial Distribution models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

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What is a Geometric Distribution?

Back

A Geometric Distribution models the number of trials needed to achieve the first success in a series of independent Bernoulli trials.

Front

What is the formula for Binomial Probability?

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P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success.

Front

What is the formula for Geometric Probability?

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P(X = k) = (1-p)^(k-1) * p, where k is the trial on which the first success occurs and p is the probability of success.

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In a Binomial Distribution, what does 'n' represent?

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'n' represents the number of trials or experiments conducted.

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In a Geometric Distribution, what does 'p' represent?

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'p' represents the probability of success on each trial.

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What is the expected value of a Binomial Distribution?

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The expected value (mean) is E(X) = n * p.

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What is the expected value of a Geometric Distribution?

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The expected value (mean) is E(X) = 1/p.

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How do you calculate the probability of 'at least' k successes in a Binomial Distribution?

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P(X >= k) = 1 - P(X < k) = 1 - P(X <= k-1).

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How do you calculate the probability of 'at least' one success in a Geometric Distribution?

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P(X >= 1) = 1 - P(X = 0) = 1 - (1-p)^k.