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 characterized by the number of trials (n) and the probability of success (p).

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

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

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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 at most k successes in n trials.

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What is the formula for calculating the probability of exactly k successes in a Binomial Distribution?

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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 is the mean of a Binomial Distribution?

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The mean (expected value) of a Binomial Distribution is given by the formula μ = 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 given by the formula σ² = n * p * (1 - p).

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What is the difference between a discrete and a continuous random variable?

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A discrete random variable can take on a countable number of values, while a continuous random variable can take on an infinite number of values within a given range.

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Give an example of a discrete random variable.

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The number of heads in 10 coin flips is a discrete random variable.

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Give an example of a continuous random variable.

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The time it takes for a student to complete an exam is a continuous random variable.