Topic 4.8 binomial distributions (pdf and cdf)

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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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What does 'cdf' stand for in statistics?

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'cdf' stands for cumulative distribution function, which gives the probability that a random variable is less than or equal to a certain value.

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What does 'pdf' stand for in statistics?

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'pdf' stands for probability density function, which describes the likelihood of a random variable to take on a particular value.

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What is the formula for the binomial probability?

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The formula for binomial probability is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success.

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How do you calculate the probability of getting more than k successes in a binomial distribution?

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To calculate the probability of getting more than k successes, you can use the complement rule: P(X > k) = 1 - P(X ≤ k), where P(X ≤ k) can be found using the cumulative distribution function.

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What is the significance of the parameters n and p in a binomial distribution?

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In a binomial distribution, 'n' represents the number of trials, and 'p' represents the probability of success on each trial.

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How do you find the probability of at most k successes in a binomial distribution?

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To find the probability of at most k successes, you use the cumulative distribution function: P(X ≤ k) = Σ (n choose i) * p^i * (1-p)^(n-i) for i = 0 to k.

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What is the expected value 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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What is the probability of getting exactly k successes in n trials?

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The probability of getting exactly k successes in n trials is given by the binomial probability formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k).