Chapter 6 Discrete Probability Distributions

Probability Distribution: a listing of all the outcomes of an experiment and the probability associated w/ each outcome.

Characteristics of a Probability Distribution

1. Probability of a particular outcome is between 0 and 1 inclusive.
2. Outcomes are mutually exclusive
3. List of outcomes is exhaustive. So the sum of probabilities of the outcomes is equal to 1.

Random variable: a variable measured or observed as the result of an experiment.

Discrete random variable: a random variable that can assume only certain clearly separated values.

Continuous random variable: a random variable that may assume an infinite number of values within a given range.

Binomial Probability Distribution:

Characteristics of a binomial probability experiment

1. An outcome on each trial of an experiment is classified into one of two mutually exclusive categories - a success or a failure.
2. The random variable is the number of successes in a fixed number of trials.
3. The probability of success is the same for each trial.
4. The trials are independent, meaning that the outcome of a trial does not affect the outcome of any other trial.

Hypergeometric Probability Distribution:

For the binomial distribution to be applied, the probability of a success must stay the same for each trial. The hypergeometric distribution is used when 1) the sample is selected from a finite population without replacement and 2) if the size of the sample n is more than 5% of the size of the population of N.

Characteristics of a hypergeometric probability experiment

1. An outcome on each trial of an experiment is classified into one of two mutually exclusive categories - a success or a failure.
2. The random variable is the number of successes in a fixed number of trials.
3. The trials are not independent.
4. We assume that we sample from a finite population without replacement and n/N > 0.05. So, the probability of a success changes for each trial.

Poisson Probability Distribution

The Poisson probability distribution describes the number of times some event occurs during a specified interval. Examples of an interval may be time, distance, area, or volume.

The distribution is based on two assumptions. The first assumption is that the probability is proportional to the length of the interval. The second assumption is that the intervals are independent.

Characteristics of a poisson probability experiment

1. The random variable is the number of times some event occurs during a defined interval.
2. The probability of the event is proportional to the size of the interval.
3. The intervals do not overlap and are independent.