Binomial Distribution: HUNTER

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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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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What are the parameters of a Binomial Distribution?

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The parameters of a Binomial Distribution are n (the number of trials) and p (the probability of success on each trial).

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What does X ~ B(n, p) represent?

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X ~ B(n, p) indicates that the random variable X follows a Binomial Distribution with n trials and a probability p of success.

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How do you calculate the probability of exactly k successes in a Binomial Distribution?

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The probability of exactly k successes in a Binomial Distribution is calculated using the formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k).

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What does P(X = k) mean in the context of Binomial Distribution?

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P(X = k) represents the probability of obtaining exactly k successes in n independent Bernoulli trials.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What is the significance of the probability of success (p) in a Binomial Distribution?

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The probability of success (p) determines how likely it is to achieve a success in each trial, influencing the shape and spread of the distribution.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What is the mean of a Binomial Distribution?

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The mean (expected value) of a Binomial Distribution is calculated as E(X) = n * p.

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What is the variance of a Binomial Distribution?

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

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What does P(X > k) represent?

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P(X > k) represents the probability of obtaining more than k successes in n trials.

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CCSS.HSS.MD.B.6

CCSS.HSS.MD.B.7

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What does P(X ≤ k) represent?

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P(X ≤ k) represents the probability of obtaining k or fewer successes in n trials.