6.3 Flashcard Binomial and Geometric Distributions Make-Up

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 states and is defined by the number of trials (n) and the probability of success (p).

Front

What is a geometric distribution?

Back

A geometric distribution models the number of trials needed to achieve the first success in a series of independent Bernoulli trials, characterized by a constant probability of success (p).

Front

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

Back

In a binomial distribution, 'n' represents the number of independent trials or experiments.

Front

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

Back

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

Front

What is the formula for calculating the probability of exactly k successes in a binomial distribution?

Back

P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where 'n choose k' is the binomial coefficient.

Front

What is the mean of a binomial distribution?

Back

The mean of a binomial distribution is calculated as μ = n * p.

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What is the standard deviation of a binomial distribution?

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The standard deviation of a binomial distribution is calculated as σ = √(n * p * (1 - p)).

Front

What is the probability of finding the first success on the k-th trial in a geometric distribution?

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P(X = k) = (1 - p)^(k-1) * p, where 'p' is the probability of success.

Front

What is the mean of a geometric distribution?

Back

The mean of a geometric distribution is calculated as μ = 1/p.

Front

What is the standard deviation of a geometric distribution?

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The standard deviation of a geometric distribution is calculated as σ = √((1 - p) / p^2).