Probability Distribution The probability distribution for a random

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

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

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

Standard Deviation of a Discrete Probability Distribution z 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

The Binomial or Bernoulli Process z The experiment consists of n identical trials; z Each trial results in one of two outcome, success or failure; z 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 ); z The trials are independent; and z The experimenter is interested in X, the number of successes observed during the n trials.

Example: Taste Test; Coke Vs. Pepsi Sample size (n) = 3, P(Coke is preferred) = 0. 20 Simple Consumer Event One Two Three e 1 C C C e 2 C C P e 3 C P C e 4 C P P e 5 P C C e 6 P C P e 7 P P C e 8 P P(ei)_ ___ (0. 20)3 = 0. 008 (0. 20)2(0. 80) = 0. 032 (0. 20)(0. 80)2 = 0. 128 (0. 80)3 = 0. 512 1. 000

Probability Distribution Coke Vs. Pepsi _X_ ___ei___ _P(X)_ 0 e 8 0. 512 1 e 4, e 6, e 7 0. 384 2 e 2, e 3, e 5 0. 096 3 e 1 0. 008 1. 000