Geometric and Binomial Distributions

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What is a Geometric Distribution?

Back

A probability distribution that models the number of trials needed for the first success in a series of independent Bernoulli trials.

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What is a Binomial Distribution?

Back

A probability distribution that summarizes the likelihood that a value will take on one of two independent outcomes over a specified number of trials.

Front

What are the parameters of a Binomial Distribution?

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The number of trials (n) and the probability of success (p) in each trial.

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What is the formula for the probability of exactly k successes in a Binomial Distribution?

Back

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

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What does 'n choose k' mean in the context of Binomial Distribution?

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It represents the number of ways to choose k successes from n trials, calculated as n! / (k!(n-k)!).

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What is the mean of a Binomial Distribution?

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The mean (expected value) is calculated as μ = n * p.

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What is the standard deviation of a Binomial Distribution?

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The standard deviation is calculated as σ = √(n * p * (1 - p)).

Front

What is the probability of getting exactly 2 successes in 20 trials with a success probability of 0.11?

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Use the Binomial formula: P(X = 2) = (20 choose 2) * (0.11)^2 * (0.89)^(20-2) = 0.282.

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What is the assumption of independence in Binomial Distribution?

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Each trial must be independent, meaning the outcome of one trial does not affect the others.

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What is the assumption of success/failure in Binomial Distribution?

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Each trial must result in a success or a failure, with no other outcomes.