Binomial Vs Geometric Distributions

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 get the first success in a series of independent Bernoulli trials.

Front

When would you use a Binomial Distribution?

Back

Use a Binomial Distribution when you have a fixed number of trials, each with two possible outcomes (success or failure), and you want to find the probability of a certain number of successes.

Front

When would you use a Geometric Distribution?

Back

Use a Geometric Distribution when you are interested in the number of trials until the first success occurs.

Front

What is the formula for Binomial Probability?

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

What is the formula for Geometric Probability?

Back

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

Rolling a die until you get a 4.

Front

What does 'n' represent in Binomial Distribution?

Back

In Binomial Distribution, 'n' represents the number of trials.

Front

What does 'p' represent in both distributions?

Back

In both distributions, 'p' represents the probability of success on each trial.