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Introduction to Statistics and Data Analysis

Roxy Peck, Chris Olsen, Jay Devore

Chapter 7

Random Variables and Probability Distributions - all with Video Answers

Educators

Section 1

Random Variables

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Problem 1

State whether each of the following random variables is discrete or continuous:
a. The number of defective tires on a car
b. The body temperature of a hospital patient
c. The number of pages in a book
d. The number of draws (with replacement) from a deck of cards until a heart is selected
e. The lifetime of a lightbulb

Rashmi Sinha
Rashmi Sinha
Numerade Educator
02:02

Problem 2

Classify each of the following random variables as either discrete or continuous:
a. The fuel efficiency (mpg) of an automobile
b. The amount of rainfall at a particular location during the next year
c. The distance that a person throws a baseball
d. The number of questions asked during a l-hour lecture
e. The tension (in pounds per square inch) at which a tennis racket is strung
f. The amount of water used by a household during a given month
g. The number of traffic citations issued by the highway patrol in a particular county on a given day

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
03:41

Problem 3

Starting at a particular time, each car entering an intersection is observed to see whether it turns left (L) or right (R) or goes straight ahead (S). The experiment terminates as soon as a car is observed to go straight. Let $y$ denote the number of cars observed.
a. What are possible $y$ values?
b. List five different outcomes and their associated $y$ values. (Hint: See Example 7.2.)

EW
Eileen Wolfe
Numerade Educator
01:43

Problem 4

A point is randomly selected from the interior of the square pictured.
Let $x$ denote the distance from the lower left-hand corner $A$ of the square to the selected point.
a. What are possible values of $x ?$
b. Is $x$ a discrete or a continuous variable? (Hint: See

Lucas Finney
Lucas Finney
Numerade Educator
10:31

Problem 5

A point is randomly selected on the surface of a lake that has a maximum depth of 100 feet. Let $y$ be the depth of the lake at the randomly chosen point.
a. What are possible values of $y$ ?
b. Is $y$ discrete or continuous?

Jacquelinne S. Mejia Sandoval
Jacquelinne S. Mejia Sandoval
Numerade Educator
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Problem 6

A person stands at the corner marked $A$ of the square pictured in Exercise $7.4$ and tosses a coin. If it lands heads up, the person moves one corner clockwise, to $B$. If the coin lands tails up, the person moves one corner counterclockwise, to $D$. This process is then repeated until the person arrives back at $A$. Let $y$ denote the number of coin tosses.
a. What are possible values of $y$ ?
b. Is $y$ discrete or continuous?

Victor Salazar
Victor Salazar
Numerade Educator
07:01

Problem 7

A box contains four slips of paper marked $1,2,3$, and 4 . Two slips are selected without replacement. List the possible values for each of the following random variables:
a. $x=$ sum of the two numbers
b. $y=$ difference between the first and second numbers
c. $z=$ number of slips selected that show an even number
d. $w=$ number of slips selected that show a 4

Lourence Gonhovi
Lourence Gonhovi
Numerade Educator