Geometric vs. Binomial

Front

What is a binomial random variable?

Back

A binomial random variable is a type of discrete random variable that counts the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

Front

What are the parameters of a binomial distribution?

Back

The parameters of a binomial distribution are n (the number of trials) and p (the probability of success on each trial).

Front

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

Back

P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where (n choose k) = n! / (k!(n-k)!).

Front

What does it mean for trials to be independent in a binomial distribution?

Back

It means that the outcome of one trial does not affect the outcome of another trial.

Front

What is the expected value (mean) of a binomial distribution?

Back

The expected value (mean) of a binomial distribution is given by E(X) = n * p.

Front

What is the variance of a binomial distribution?

Back

The variance of a binomial distribution is given by Var(X) = n * p * (1 - p).

Front

How do you find the cumulative probability for a binomial distribution?

Back

To find the cumulative probability for a binomial distribution, sum the probabilities of getting k or fewer successes: P(X ≤ k) = Σ P(X = i) for i = 0 to k.

Front

What is the difference between a geometric distribution and a binomial distribution?

Back

A geometric distribution models the number of trials until the first success, while a binomial distribution models the number of successes in a fixed number of trials.

Front

What is the probability of success in a binomial distribution?

Back

The probability of success in a binomial distribution is denoted by p and can range from 0 to 1.

Front

What is a Bernoulli trial?

Back

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