Binomial Distribution

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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: n (number of trials) and p (probability of success).

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What does 'n' represent in a Binomial Distribution?

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'n' represents the number of independent trials or experiments in a Binomial Distribution.

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What does 'p' represent in a Binomial Distribution?

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'p' represents the probability of success on a single trial in a Binomial Distribution.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What is the formula for the probability mass function (PMF) of a Binomial Distribution?

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The PMF is given by P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where k is the number of successes.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What is the cumulative distribution function (CDF) in the context of Binomial Distribution?

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The CDF gives the probability that the random variable X is less than or equal to a certain value k, denoted as P(X ≤ k).

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CCSS.HSS.ID.A.4

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

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To find the probability of at least k successes, use P(X ≥ k) = 1 - P(X < k) = 1 - binomialcdf(n, p, k-1).

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CCSS.HSS.MD.A.2

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What is the difference between binompdf and binomcdf?

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binompdf(n, p, k) calculates the probability of exactly k successes, while binomcdf(n, p, k) calculates the cumulative probability of k or fewer successes.

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What is the expected value (mean) of a Binomial Distribution?

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

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CCSS.HSS.MD.A.2

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What is the variance of a Binomial Distribution?

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The variance is calculated as Var(X) = n * p * (1 - p).

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What is the geometric distribution?

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The geometric distribution models the number of trials until the first success in a series of independent Bernoulli trials.