1. Binomial Distribution
The binomial distribution is a discrete distribution.

2. Binomial Experiment
A binomial experiment has the following properties:
experiment consists of n identical and independent trials
each trial results in one of two outcomes: success or failure
P(success) = p
P(failure) = q = 1 - p for all trials
The random variable of interest, X, is the number of successes in the n trials.
X has a binomial distribution with parameters n and p

3. EXAMPLES A coin is flipped 10 times. Success = head. X = n = p =
Twelve pregnant women selected at random, take a home pregnancy test. Success = test says pregnant.
X = n = p = ?
Random guessing on a multiple choice exam. 25 questions. 4 answers per question. Success = right answer.

4. Examples when assumptions do not hold
Basketball player shoots ten free throws
Feedback affects independence and constant p
Barrel contains 3 red apples and 4 green apples; select 4 apples without replacement; X = # of red apples.
Without replacement implies dependence

5. What is P(x) for binomial?

6. Mean and Standard Deviation
The mean (expected value) of a binomial random variable is
The standard deviation of a binomial random variable is

7. Example Random Guessing; n = 100 questions. Expected Value =
Probability of correct guess; p = 1/4
Probability of wrong guess; q = 3/4
Expected Value =
On average, you will get 25 right.
Standard Deviation =

8. Example Cancer Treatment; n = 20 patients
Probability of successful treatments; p = 0.7
Probability of no success; q = ?
Calculate the mean and standard deviation.

9. Normal Approximation
For large n, the binomial distribution can be approximated by the normal,
is approximately standard normal for large n.