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1. Copyright © 2017 Pearson Education, Ltd. Chapter 5, Slide 1
Chapter 5
Discrete Random
Variables
Copyright © 2017 Pearson Education, Ltd. Chapter 5, Slide 1

2. Copyright © 2017 Pearson Education, Ltd. Chapter 5, Slide 2
Chapter 5
Discrete Random Variables

3. Copyright © 2017 Pearson Education, Ltd. Chapter 5, Slide 3
Section 5.1
Discrete Random Variables
and Probability Distributions

4. Copyright © 2017 Pearson Education, Ltd. Chapter 5, Slide 4
Definitions 5.1 & 5.2
Random Variable
A random variable is a quantitative variable whose value
depends on chance.
Discrete Random Variable
A discrete random variable is a random variable whose
possible values can be listed. In particular, a random
variable with only a finite number of possible values is a
discrete random variable.

5. Copyright © 2017 Pearson Education, Ltd. Chapter 5, Slide 5
{X = 4}
X = number of siblings of a randomly selected
student.
P(X=4)

6. Copyright © 2017 Pearson Education, Ltd. Chapter 5, Slide 6
Definition 5.3
Probability Distribution and Probability Histogram
Probability distribution: A listing of the possible values
and corresponding probabilities of a discrete random
variable, or a formula for the probabilities.
Probability histogram: A graph of the probability
distribution that displays the possible values of a discrete
random variable on the horizontal axis and the
probabilities of those values on the vertical axis. The
probability of each value is represented by a vertical bar
whose height equals the probability.

7. Copyright © 2017 Pearson Education, Ltd. Chapter 5, Slide 7
Table 5.2 & Figure 5.1
Probability distribution of the
random variable X, the number
of siblings of a randomly
selected student
Probability histogram for the random
variable X, the number of siblings of
a randomly selected student

8. Copyright © 2017 Pearson Education, Ltd. Chapter 5, Slide 8
Key Fact 5.1

9. Copyright © 2017 Pearson Education, Ltd. Chapter 5, Slide 9
Key Fact 5.2
Interpretation of a Probability Distribution
In a large number of independent observations of a random
variable X, the proportion of times each possible value occurs
will approximate the probability distribution of X; or,
equivalently, the proportion histogram will approximate the
probability histogram for X.

10. Copyright © 2017 Pearson Education, Ltd. Chapter 5, Slide 10
Figure 5.2
(a) Histogramof proportions for the numbers of heads obtained in three tosses of
a balanced dime for 1000 observations; (b) probability histogram for the number
of heads obtained in three tosses of a balanced dime

11. Copyright © 2017 Pearson Education, Ltd. Chapter 5, Slide 11
Section 5.3
The Binomial Distribution

12. Copyright © 2017 Pearson Education, Ltd. Chapter 5, Slide 12
Testing the effectiveness of a drug:
1. effective
2. not effective
Born of baby is BOY
1.YES
2. NO
Taste test for coca-cola:
1. first coca-cola
2. second coca-cola.

13. Copyright © 2017 Pearson Education, Ltd. Chapter 5, Slide 13
Definition 5.6
5! = 5x4x3x2x1

14. Copyright © 2017 Pearson Education, Ltd. Chapter 5, Slide 14
Definition 5.7
(a+b)n

15. Copyright © 2017 Pearson Education, Ltd. Chapter 5, Slide 15
Section 5.4
The Poisson Distribution

16. Copyright © 2017 Pearson Education, Ltd. Chapter 5, Slide 16
Formula 5.3

17. Copyright © 2017 Pearson Education, Ltd. Chapter 5, Slide 17
ƛ = 6.9
P(X≤2) = P(X=0)+P(X=1)+P(X=2) = 0.032
e(2.718) -6.9 (6.9)0
0!