The Binomial Distribution

The binomial setting:

1. Each observation falls into one categories: Success or Failure

2. There are a fixed number of observations n.

3. The n observations are all independent.

4. The probability of success, call it p, is the same for each observation.


The distribution of the count X of successes in the binomial setting is the binomial distribution with parameters n and p. The parameter n is the number of observations, and p is the probability of a success on any one observation. The possible values of X are the whole numbers from 0 to n. As an abbreviation, we say that X is B(n,p).

PDF = Probability distribution function

Discuss the Binomial Coefficient and then introduce Binomial probability.

Now go back to the coin toss experiment and try to predict the probability of the outcomes, where the getting heads is a success and tails is a failure for a fixed number of tosses. This is very obvious that the probability is 50% but it will allow the students to begin to understand the binomial distribution. Later on work more complicated examples.

Bring Mean and Standard deviation into the picture. Show this graphically.

Mean = np

Standard Deviation = square root(np(1- p))