Geometric and Binomial Distributions

Front

What is a Geometric Distribution?

Back

A probability distribution that models the number of trials needed to get the first success in a series of independent Bernoulli trials.

Front

What is a Binomial Distribution?

Back

A probability distribution that models the number of successes in a fixed number of independent Bernoulli trials.

Front

What are the parameters of a Binomial Distribution?

Back

The number of trials (n) and the probability of success (p) in each trial.

Front

What is the formula for the probability of exactly k successes in a Binomial Distribution?

Back

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

Front

What is the mean of a Binomial Distribution?

Back

The mean is given by μ = n * p.

Front

What is the variance of a Binomial Distribution?

Back

The variance is given by σ² = n * p * (1 - p).

Front

What is the standard deviation of a Binomial Distribution?

Back

The standard deviation is σ = √(n * p * (1 - p)).

Front

What is the difference between Binomial and Geometric Distributions?

Back

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

Front

What is the probability of getting exactly 2 successes in 20 trials with a success probability of 0.11?

Back

0.282 (using the Binomial formula).

Front

What does it mean for trials to be independent in a Binomial experiment?

Back

The outcome of one trial does not affect the outcome of another trial.