Geometric vs. Binomial

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, 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 of success in a geometric distribution?

Back

The probability of success in a geometric distribution is denoted as 'p'.

Front

What is the formula for the expected value of a geometric distribution?

Back

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

Front

What is the formula for the probability of getting exactly k successes in a binomial distribution?

Back

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

Front

What does 'n choose k' mean in the context of binomial distribution?

Back

'n choose k' refers to the number of ways to choose k successes from n trials, calculated as n! / (k!(n-k)!).

Front

What is the variance of a binomial distribution?

Back

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

Front

How do you determine the number of trials needed in a geometric distribution?

Back

The number of trials needed is determined by the formula E(X) = 1/p, where p is the probability of success.

Front

What is the cumulative distribution function (CDF) of a geometric distribution?

Back

The CDF of a geometric distribution gives the probability that the first success occurs on or before the k-th trial, calculated as P(X ≤ k) = 1 - (1-p)^k.

Front

What is the relationship between geometric and binomial distributions?

Back

Geometric distribution is concerned with the number of trials until the first success, while binomial distribution deals with a fixed number of trials and counts the number of successes.