Lesson 4.1 Discrete Probability Distributions: An Introduction

Random Variable

A random variable assigns values to the outcomes of a statistical experiment. Upper case letters denote random variables.

Example:

• Let X = the number of cars in a household.
• Let Y = the amount of time (in minutes) a college students waits in line at the cafeteria.

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Discrete Random Variable

A discrete random variable is a random variable that assigns countable values to the outcomes of a statistical experiment. Often the phrase "the number of" is used in the description of a discrete random variable.

Example:

• Let X = the number of patients cured from a particular disease.
• Let Y = the number of questions that a statistics student answers correctly on the first exam.

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Discrete Probability Distribution Function (Discrete PDF)

A discrete probability distribution function (discrete PDF) consists of

• countable numerical values.
• probabilities for those numerical values. The sum of the probabilites is 1.

Example: A controversial drug is given to TWO patients to cure a particular disease.

P(a cure for each patient) = 5/6.

P(no cure for each patient) = 1/6.

 

Let X = the number of patients (out of two) cured. Then, because one patient being cured is independent of the other patient being cured, we have:

P(0 patients out of two cured)

= P(1st person not cured)*P(2nd person not cured)

= (1/6)(1/6) = 1/36

P(1 out of two cured)

= P(1st person cured)*P(2nd person not cured) +

P(2nd person cured)*P(1st person not cured)

= (5/6)(1/6) + (1/6)(5/6) = 10/36

P(both patients cured)

= P(1st person cured)*P(2nd person cured)

= (5/6)(5/6) = 25/36

We can represent the discrete PDF in a table:

Notice that (1/36) + (10/36) + (25/36) = 1.

Please continue to the next section of this lesson.

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Up » 4.1 Discrete Probability » 4.2 Expected Value » 4.3 Binomial Probability » 4.4 Poisson Probability

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