1. Probability Distribution
The probability distribution for a random variable is an assignment of probability to each of the possible values for the variable

2. Probability Distributions
Discrete Probability Distributions
1. The Uniform Distribution;
2. The Binomial Distribution;
3. The Hypergeometric Distribution; and
4. The Poisson Distribution
Continuous Probability Distributions
1. The Uniform Distribution; and
2. The Normal Distribution

3. Mean of a Discrete Probability Distribution
The mean of a discrete probability distribution is also called the expected value of the discrete random variable.
where, E(X) = expected value of X
X = values of the random variable
P(X) = probability of each value of X

4. Standard Deviation of a Discrete Probability Distribution
Standard Deviation of a discrete random variable
where, X = values of the random variable
E(X) = expected value of X
P(X) = probability of each value of X

5. The Binomial or Bernoulli Process
The experiment consists of n identical trials;
Each trial results in one of two outcome, success or failure;
The probability of success on a single trial is equal to p, and remains the same from trial to trial. The probability of failure is ( 1 - p );
The trials are independent; and
The experimenter is interested in X, the number of successes observed during the n trials.

6. Example: Taste Test; Coke Vs
Example: Taste Test; Coke Vs. Pepsi Sample size (n) = 3, P(Coke is preferred) = 0.20
Simple Consumer
Event One Two Three P(ei)_ ___
e1 C C C (0.20)3 = 0.008
e2 C C P (0.20)2(0.80) = 0.032
e C P C (0.20)2(0.80) = 0.032
e4 C P P (0.20)(0.80)2 = 0.128
e5 P C C (0.20)2(0.80) = 0.032
e6 P C P (0.20)(0.80)2 = 0.128
e7 P P C (0.20)(0.80)2 = 0.128
e8 P P P (0.80)3 = 0.512
1.000

7. Probability Distribution
Coke Vs. Pepsi
_X_ ___ei___ _P(X)_ e
1 e4,e6,e
e2,e3,e e
1.000