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CHAPTER 7
Section 7.1 – Discrete and Continuous Random
Variables
INTRODUCTION
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Sample spaces need not consist of numbers. When
we toss four coins, we can record the outcomes as a
string of heads and tails, such as HTTH.
Recall from chapter 6 that a random variable is
defined as a variable whose value is a numerical
outcome of a random phenomenon.
In this section we will learn two ways of assigning
probabilities to the values of a random variable.
Discrete
 Continuous
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DISCRETE RANDOM VARIABLE
A discrete random variable X has a countable number of possible
values.
The probability distribution of X lists the values xi and their
probabilities pi:
Value of X:
Probability:
x1 x2
p1 p2
x3
p3
…
…
The probabilities pi must satisfy two requirements:
1. Every probability pi is a number between 0 and 1.
2. The sum of the probabilities is 1.
To find the probability of any event, add the probabilities pi of the
particular values xi that make up the event.
EXAMPLE 7.1 - GETTING GOOD GRADES
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See example 7.1 on p.392
Probability histograms can be used to display
probability distributions.
When using a histogram the height of each bar shows
the probability of the outcome at its base.
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Because the heights are probabilities, they add up to 1.
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The bars are the same width.
EXAMPLE 7.2 – TOSSING COINS
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See example 7.2 on p.394-395
CONTINUOUS RANDOM VARIABLE
A continuous random variable X takes all values in an interval of
numbers.
The probability distribution of X is described by a density curve.
The probability of any event is the area under the density curve and
above the values of X that make up the event.
EXAMPLE 7.3 – RANDOM NUMBERS AND THE
UNIFORM DISTRIBUTION
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See example 7.3 on p.398
CONTINUOUS RANDOM VARIABLES
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We assign probabilities directly to events – as areas
under a density curve. Any density curve has area
exactly 1 underneath it, corresponding to total
probability 1.
All continuous probability distributions assign
probability of 0 to every individual outcome.
 Read p.399 for an explanation
We can ignore the distinction between < and ≤ when
finding probabilities for continuous random variables.
We can see why an outcome exactly to .8 should have
probability of 0.
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Homework: p.396-405 #’s 2, 3, 6, 7, 10, 11, 14, 16,
& 17