Page 126 - Probability Demystified

CHAPTER 7 The Binomial Distribution 115

Discrete Probability Distributions

In mathematics, a variable can assume different values. For example, if one
records the temperature outside every hour for a 24-hour period, temperature
is considered a variable since it assumes different values. Variables whose
values are due to chance are called random variables. When a die is rolled, the
value of the spots on the face up occurs by chance; hence, the number of
spots on the face up on the die is considered to be a random variable. The
outcomes of a die are 1, 2, 3, 4, 5, and 6, and the probability of each outcome
1
occurring is . The outcomes and their corresponding probabilities can be
6
written in a table, as shown, and make up what is called a probability
distribution.

Value, x 1 2 3 4 5 6
1 1 1 1 1 1
Probability, P(x)
6 6 6 6 6 6

A probability distribution consists of the values of a random variable and
their corresponding probabilities.

There are two kinds of probability distributions. They are discrete and
continuous.A discrete variable has a countable number of values (countable
means values of zero, one, two, three, etc.). For example, when four coins are
tossed, the outcomes for the number of heads obtained are zero, one, two,
three, and four. When a single die is rolled, the outcomes are one, two, three,
four, five, and six. These are examples of discrete variables.
A continuous variable has an infinite number of values between any two
values. Continuous variables are measured. For example, temperature is a
continuous variable since the variable can assume any value between 108 and
208 or any other two temperatures or values for that matter. Height and
weight are continuous variables. Of course, we are limited by our measuring
devices and values of continuous variables are usually ‘‘rounded off.’’
EXAMPLE: Construct a discrete probability distribution for the number of
heads when three coins are tossed.

SOLUTION:
Recall that the sample space for tossing three coins is
TTT, TTH, THT, HTT, HHT, HTH, THH, and HHH.