Binomial Distributions #1

Front

What is a binomial distribution?

Back

A binomial distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent outcomes under a given set of parameters.

Front

What are the parameters of a binomial distribution?

Back

The parameters of a binomial distribution are n (the number of trials) and p (the probability of success on an individual trial).

Front

What is the formula for calculating the probability of getting exactly k successes in n trials?

Back

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

Front

In a binomial experiment, what does 'n' represent?

Back

'n' represents the number of trials or experiments conducted.

Front

In a binomial experiment, what does 'p' represent?

Back

'p' represents the probability of success on a single trial.

Front

What is the mean of a binomial distribution?

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The mean (expected value) of a binomial distribution is calculated as 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 calculated as σ² = n * p * (1 - p).

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

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To find the probability of getting at least k successes, calculate P(X ≥ k) = 1 - P(X < k).

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What is the difference between independent and dependent trials in a binomial experiment?

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Independent trials mean the outcome of one trial does not affect the outcome of another, while dependent trials do affect each other.

Front

Is the following scenario a binomial experiment? Flipping a coin 10 times. Let X = the number of heads observed.

Back

Yes, this is a binomial experiment because there are two outcomes (heads or tails), and each flip is independent.