Geometric vs. Binomial

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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).

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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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).

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How do you calculate the mean of a binomial distribution?

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The mean of a binomial distribution is calculated using the formula: mean = 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: standard deviation = √(n * p * (1 - p)).

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What is the cumulative probability in a binomial distribution?

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Cumulative probability in a binomial distribution is the probability that the random variable is less than or equal to a certain value, calculated by summing the probabilities of all outcomes up to that value.

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What is the expected value in a geometric distribution?

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The expected value (mean) in a geometric distribution is calculated using the formula: expected value = 1/p, where p is the probability of success.

Tags

CCSS.HSS.MD.A.2

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What does it mean if a distribution is skewed right?

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A distribution is skewed right if it has a longer tail on the right side, indicating that there are a few high values that are pulling the mean to the right.

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What is the probability of getting exactly k successes in a binomial distribution?

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

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What is the probability of the first success occurring on the k-th trial in a geometric distribution?

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The probability of the first success occurring on the k-th trial in a geometric distribution is given by the formula: P(X = k) = (1 - p)^(k - 1) * p.

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What is the relationship between binomial and geometric distributions?

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The binomial distribution counts the number of successes in a fixed number of trials, while the geometric distribution counts the number of trials until the first success.