Binomial Probability Distribution #2

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What is a Binomial Probability Distribution?

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A Binomial Probability Distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

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

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'n choose k' (denoted as C(n, k) or nCk) represents the number of ways to choose k successes from n trials and is calculated as n! / (k!(n-k)!).

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What is the probability of getting at least k successes?

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The probability of getting at least k successes is calculated by summing the probabilities of getting k, k+1, ..., n successes.

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In a Binomial Distribution, what does it mean if p = 0.5?

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If p = 0.5, it means that the probability of success and failure are equal, leading to a symmetric distribution.

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

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The expected value (mean) 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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How do you find the probability of more than k successes?

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To find the probability of more than k successes, calculate P(X > k) = 1 - P(X ≤ k), where P(X ≤ k) is the cumulative probability up to k.

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

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The cumulative distribution function (CDF) gives the probability that a random variable X is less than or equal to a certain value k.