Geometric vs. Binomial

Front

What is a geometric distribution?

Back

A geometric distribution models the number of trials until the first success in a series of independent Bernoulli trials, where each trial has the same probability of success.

Front

What is a binomial distribution?

Back

A binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

Front

What is the probability formula for a geometric distribution?

Back

P(X = k) = (1-p)^(k-1) * p, where p is the probability of success and k is the trial number of the first success.

Front

What is the probability formula for a binomial distribution?

Back

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.

Front

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

Back

'n' represents the number of independent trials conducted.

Front

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

Back

'p' represents the probability of success on each trial.

Front

What is the expected value of a geometric distribution?

Back

The expected value (mean) of a geometric distribution is E(X) = 1/p.

Front

What is the expected value of a binomial distribution?

Back

The expected value (mean) of a binomial distribution is E(X) = n * p.

Front

How do you determine if a situation is modeled by a geometric distribution?

Back

A situation is modeled by a geometric distribution if you are counting the number of trials until the first success occurs.

Front

How do you determine if a situation is modeled by a binomial distribution?

Back

A situation is modeled by a binomial distribution if you are counting the number of successes in a fixed number of trials.