Ch 17 Binomial v. Geometric DIstribution

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 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.

Front

What are the key characteristics of a Binomial Distribution?

Back

1. Fixed number of trials (n). 2. Two possible outcomes (success or failure). 3. Constant probability of success (p). 4. Trials are independent.

Front

What are the key characteristics of a Geometric Distribution?

Back

1. Trials continue until the first success. 2. Two possible outcomes (success or failure). 3. Constant probability of success (p). 4. Trials are independent.

Front

In a Binomial Distribution, how do you calculate the probability of exactly k successes?

Back

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

Front

In a Geometric Distribution, how do you calculate the probability of the first success on the k-th trial?

Back

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

Front

What is the difference between Binomial and Geometric Distributions?

Back

Binomial Distribution is used for a fixed number of trials, while Geometric Distribution is used for trials until the first success.

Front

Example of a Binomial Distribution scenario.

Back

Flipping a coin 10 times and counting the number of heads.

Front

Example of a Geometric Distribution scenario.

Back

Flipping a coin until the first head appears.

Front

What is the mean of a Binomial Distribution?

Back

Mean (μ) = n * p, where n is the number of trials and p is the probability of success.