Is Amount of Rain in Inchese Discrete or Continuous
Chapter 6
Random Variables and Probability Distributions - all with Video Answers
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
Problem 2
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 $x$ denote the number of cars observed. What are possible $x$ values? List five different outcomes and their associated $x$ values. (Hint: See Example 6.2)
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
Problem 4
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 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
Problem 5
A point is randomly selected from the interior of a square, as pictured:
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?
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?
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
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?
Problem 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
Source: https://www.numerade.com/books/chapter/random-variables-and-probability-distributions-3/
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