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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 outcomes under a given number of trials.

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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 an individual trial).

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What does P(X=k) represent in a Binomial Distribution?

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P(X=k) represents the probability of getting exactly 'k' successes in 'n' trials.

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What is the formula for calculating Binomial Probability?

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The formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where (n choose k) = n! / (k!(n-k)!).

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What does the term 'success' mean in the context of Binomial Distribution?

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In Binomial Distribution, 'success' refers to the outcome of interest, which can vary depending on the context of the problem.

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What is the difference between P(X≤k) and P(X

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P(X≤k) includes the probability of getting 'k' successes, while P(X

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How do you interpret P(X>k)?

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

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

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The CDF gives the probability that a random variable is less than or equal to a certain value, allowing for the calculation of probabilities for ranges of outcomes.

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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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What is the variance of a Binomial Distribution?

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