Geometric vs. Binomial

Front

What is the definition of 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 the probability of success in a geometric distribution?

Back

The probability of success (p) is the likelihood of achieving the desired outcome in a single trial.

Front

How do you calculate the probability of exactly k successes in a binomial distribution?

Back

Use the formula 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

What is the difference between geometric and binomial distributions?

Back

Geometric distribution focuses on the number of trials until the first success, while binomial distribution counts the number of successes in a fixed number of trials.

Front

What is the expected value of a geometric distribution?

Back

The expected value (mean) of a geometric distribution is 1/p, where p is the probability of success.

Front

What is the variance of a binomial distribution?

Back

The variance of a binomial distribution is n * p * (1-p), where n is the number of trials and p is the probability of success.

Front

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

Back

Calculate P(X >= k) = 1 - P(X < k) = 1 - Σ P(X = i) for i = 0 to k-1.

Front

What is the cumulative distribution function (CDF) for a binomial distribution?

Back

The CDF gives the probability that a random variable X is less than or equal to a certain value k, calculated as P(X ≤ k) = Σ P(X = i) for i = 0 to k.

Front

What is the formula for the mean of a binomial distribution?

Back

The mean of a binomial distribution is given by μ = n * p, where n is the number of trials and p is the probability of success.

Front

What is a Bernoulli trial?

Back

A Bernoulli trial is a random experiment with exactly two possible outcomes: success or failure.