Chapter 6, Random Variables and Probability Distributions Video Solutions, Statistics Learning From Data

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 light bulb

Rashmi Sinha

Numerade Educator

03:41

Problem 2

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

Eileen Wolfe

Numerade Educator

07:01

Problem 3

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 (first $-$ second)
c. $z=$ number of slips selected that show an even number
d. $w=$ number of slips selected that show a 4

Lourence Gonhovi

Numerade Educator

02:02

Problem 4

Classify each of the following random variables as either discrete or continuous:
a. The fuel efficiency (miles per gallon) 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 1-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

Numerade Educator

01:43

Problem 5

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

Lucas Finney

Numerade Educator

03:31

Problem 6

A person stands at the corner marked $A$ of the square pictured in the previous exercise 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. What are possible values of $y ?$ Is $y$ discrete or continuous?

Manisha Sarker

Numerade Educator

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Problem 7

State whether each of the following random variables is discrete or continuous.
a. The number of courses a student is enrolled in
b. The time spent completing a homework assignment
c. The length of a person's forearm
d. The number of times out of 10 throws that a dog catches a Frisbee

Rashmi Sinha

Numerade Educator

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Problem 8

A person is asked to draw a line segment that they think is 3 inches long. The length of the line segment drawn will be measured and the value of $x=($ actual length -3$)$ will be calculated.
a. What is the value of $x$ for a person who draws a line segment that is 3.1 inches long?
b. Is $x$ a discrete or continuous random variable? Explain.

Rashmi Sinha

Numerade Educator

01:08

Problem 9

6.9 Two six-sided dice, one red and one white, will be rolled. List the possible values for each of the following random variables.
a. $x=$ sum of the two numbers showing
b. $y=$ difference between the number on the red die and the number on the white die (red - white)
c. $w=$ largest number showing

Narayan Hari

Numerade Educator