2.5.2 Binomial

Question 1

What is a binomial distribution?

Answer 1

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

Question 2

What conditions must be met for a binomial distribution?

Answer 2

1. A fixed number of trials (n).
2. Each trial has only two outcomes (success or failure).
3. The probability of success (p) is constant across trials.
4. The trials are independent of each other.

Question 3

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

Answer 3

The expected number of successes in n trials is:
E[X] = n p

Question 4

What is the variance of a binomial distribution?

Answer 4

The formula for variance is:
Var(X) = n p (1 - p)