Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. a. The number of students in a randomly selected elementary school classroom b. The amount of snow that falls in Minneapolis during the winter season c. The flight time accumulated by a randomly selected Air Force fighter pilot d. The number of points scored by the Miami Heat in a randomly selected basketball game

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Answer 1

Textbook Question

Chapter 6, Problem 1RE

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.

a. The number of students in a randomly selected elementary school classroom
b. The amount of snow that falls in Minneapolis during the winter season
c. The flight time accumulated by a randomly selected Air Force fighter pilot
d. The number of points scored by the Miami Heat in a randomly selected basketball game

(a)

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a discrete random variable.

Explanation of Solution

Given info:

The number of students in a randomly selected elementary school class room.

Justification:

Random Variable:

A random variable X is a numerical outcome of a probability experiment. Moreover, there is a numerical value which is determined by chance for each outcome in the procedure or experiment.

Discrete random variable:

A discrete random variable takes a collection of values which is finite or countable.

Denote the random variable X as “number of students in a randomly selected elementary school class room”. This is a discrete random variable because the value of the random variable is obtained from counting. That is, there can be 0,1,2,... the number of students in a randomly selected elementary school class room. Hence the possible values of the random variable X are x = 0, 1, 2, 3.... and they are all nonnegative integers.

Thus, the given random variable is a discrete random variable.

b.

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a continuous random variable.

Explanation of Solution

Given info:

The variable is “The amount of snow that falls in Minneapolis during the winter season”.

Justification:

Continuous random variable:

A continuous random variable takes infinitely many values or a collection of values which is uncountable. It is impossible to count the items as they are measured in a continuous scale.

Denote the random variable S as “The amount of snow that falls in Minneapolis during the winter season”. Here, the amount of snow that falls in Minneapolis during the winter season measured and it is a continuous random variable. Hence, the possible values of the random variable S are all positive real numbers.

So, the given random variable is a continuous random variable.

c.

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a continuous random variable.

Explanation of Solution

Given info:

The flight time accumulated by a randomly selected Air Force fighter pilot

Justification:

Denote the random variable T as “The flight time accumulated by a randomly selected Air Force fighter pilot”. This is a continuous random variable because the value of the random variable is obtained from a measurement. Hence, the possible values of the random variable T are all nonnegative real numbers.

Thus, the given random variable is a continuous random variable.

d.

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a discrete random variable.

Explanation of Solution

Given info:

The number of points scored by the Miami Heat in a randomly selected basketball game

Justification:

Denote the random variable X as “number of points scored by the Miami Heat in a randomly selected basketball game”. This is a discrete random variable because the value of the random variable is obtained from counting. That is, there can be 0,1,2,... number of points scored by the Miami Heat in a randomly selected basketball game. Hence, the possible values of the random variable X are x = 0, 1, 2, 3.... and they are all nonnegative integers.

Thus, the given random variable is a discrete random variable.

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Answer 2

Textbook Question

Chapter 6, Problem 1RE

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.

a. The number of students in a randomly selected elementary school classroom
b. The amount of snow that falls in Minneapolis during the winter season
c. The flight time accumulated by a randomly selected Air Force fighter pilot
d. The number of points scored by the Miami Heat in a randomly selected basketball game

(a)

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a discrete random variable.

Explanation of Solution

Given info:

The number of students in a randomly selected elementary school class room.

Justification:

Random Variable:

A random variable X is a numerical outcome of a probability experiment. Moreover, there is a numerical value which is determined by chance for each outcome in the procedure or experiment.

Discrete random variable:

A discrete random variable takes a collection of values which is finite or countable.

Denote the random variable X as “number of students in a randomly selected elementary school class room”. This is a discrete random variable because the value of the random variable is obtained from counting. That is, there can be 0,1,2,... the number of students in a randomly selected elementary school class room. Hence the possible values of the random variable X are x = 0, 1, 2, 3.... and they are all nonnegative integers.

Thus, the given random variable is a discrete random variable.

b.

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a continuous random variable.

Explanation of Solution

Given info:

The variable is “The amount of snow that falls in Minneapolis during the winter season”.

Justification:

Continuous random variable:

A continuous random variable takes infinitely many values or a collection of values which is uncountable. It is impossible to count the items as they are measured in a continuous scale.

Denote the random variable S as “The amount of snow that falls in Minneapolis during the winter season”. Here, the amount of snow that falls in Minneapolis during the winter season measured and it is a continuous random variable. Hence, the possible values of the random variable S are all positive real numbers.

So, the given random variable is a continuous random variable.

c.

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a continuous random variable.

Explanation of Solution

Given info:

The flight time accumulated by a randomly selected Air Force fighter pilot

Justification:

Denote the random variable T as “The flight time accumulated by a randomly selected Air Force fighter pilot”. This is a continuous random variable because the value of the random variable is obtained from a measurement. Hence, the possible values of the random variable T are all nonnegative real numbers.

Thus, the given random variable is a continuous random variable.

d.

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a discrete random variable.

Explanation of Solution

Given info:

The number of points scored by the Miami Heat in a randomly selected basketball game

Justification:

Denote the random variable X as “number of points scored by the Miami Heat in a randomly selected basketball game”. This is a discrete random variable because the value of the random variable is obtained from counting. That is, there can be 0,1,2,... number of points scored by the Miami Heat in a randomly selected basketball game. Hence, the possible values of the random variable X are x = 0, 1, 2, 3.... and they are all nonnegative integers.

Thus, the given random variable is a discrete random variable.

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Answer 3

Textbook Question

Chapter 6, Problem 1RE

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.

a. The number of students in a randomly selected elementary school classroom
b. The amount of snow that falls in Minneapolis during the winter season
c. The flight time accumulated by a randomly selected Air Force fighter pilot
d. The number of points scored by the Miami Heat in a randomly selected basketball game

(a)

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a discrete random variable.

Explanation of Solution

Given info:

The number of students in a randomly selected elementary school class room.

Justification:

Random Variable:

A random variable X is a numerical outcome of a probability experiment. Moreover, there is a numerical value which is determined by chance for each outcome in the procedure or experiment.

Discrete random variable:

A discrete random variable takes a collection of values which is finite or countable.

Denote the random variable X as “number of students in a randomly selected elementary school class room”. This is a discrete random variable because the value of the random variable is obtained from counting. That is, there can be 0,1,2,... the number of students in a randomly selected elementary school class room. Hence the possible values of the random variable X are x = 0, 1, 2, 3.... and they are all nonnegative integers.

Thus, the given random variable is a discrete random variable.

b.

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a continuous random variable.

Explanation of Solution

Given info:

The variable is “The amount of snow that falls in Minneapolis during the winter season”.

Justification:

Continuous random variable:

A continuous random variable takes infinitely many values or a collection of values which is uncountable. It is impossible to count the items as they are measured in a continuous scale.

Denote the random variable S as “The amount of snow that falls in Minneapolis during the winter season”. Here, the amount of snow that falls in Minneapolis during the winter season measured and it is a continuous random variable. Hence, the possible values of the random variable S are all positive real numbers.

So, the given random variable is a continuous random variable.

c.

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a continuous random variable.

Explanation of Solution

Given info:

The flight time accumulated by a randomly selected Air Force fighter pilot

Justification:

Denote the random variable T as “The flight time accumulated by a randomly selected Air Force fighter pilot”. This is a continuous random variable because the value of the random variable is obtained from a measurement. Hence, the possible values of the random variable T are all nonnegative real numbers.

Thus, the given random variable is a continuous random variable.

d.

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a discrete random variable.

Explanation of Solution

Given info:

The number of points scored by the Miami Heat in a randomly selected basketball game

Justification:

Denote the random variable X as “number of points scored by the Miami Heat in a randomly selected basketball game”. This is a discrete random variable because the value of the random variable is obtained from counting. That is, there can be 0,1,2,... number of points scored by the Miami Heat in a randomly selected basketball game. Hence, the possible values of the random variable X are x = 0, 1, 2, 3.... and they are all nonnegative integers.

Thus, the given random variable is a discrete random variable.

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Answer 4

Textbook Question

Chapter 6, Problem 1RE

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.

a. The number of students in a randomly selected elementary school classroom
b. The amount of snow that falls in Minneapolis during the winter season
c. The flight time accumulated by a randomly selected Air Force fighter pilot
d. The number of points scored by the Miami Heat in a randomly selected basketball game

(a)

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a discrete random variable.

Explanation of Solution

Given info:

The number of students in a randomly selected elementary school class room.

Justification:

Random Variable:

A random variable X is a numerical outcome of a probability experiment. Moreover, there is a numerical value which is determined by chance for each outcome in the procedure or experiment.

Discrete random variable:

A discrete random variable takes a collection of values which is finite or countable.

Denote the random variable X as “number of students in a randomly selected elementary school class room”. This is a discrete random variable because the value of the random variable is obtained from counting. That is, there can be 0,1,2,... the number of students in a randomly selected elementary school class room. Hence the possible values of the random variable X are x = 0, 1, 2, 3.... and they are all nonnegative integers.

Thus, the given random variable is a discrete random variable.

b.

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a continuous random variable.

Explanation of Solution

Given info:

The variable is “The amount of snow that falls in Minneapolis during the winter season”.

Justification:

Continuous random variable:

A continuous random variable takes infinitely many values or a collection of values which is uncountable. It is impossible to count the items as they are measured in a continuous scale.

Denote the random variable S as “The amount of snow that falls in Minneapolis during the winter season”. Here, the amount of snow that falls in Minneapolis during the winter season measured and it is a continuous random variable. Hence, the possible values of the random variable S are all positive real numbers.

So, the given random variable is a continuous random variable.

c.

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a continuous random variable.

Explanation of Solution

Given info:

The flight time accumulated by a randomly selected Air Force fighter pilot

Justification:

Denote the random variable T as “The flight time accumulated by a randomly selected Air Force fighter pilot”. This is a continuous random variable because the value of the random variable is obtained from a measurement. Hence, the possible values of the random variable T are all nonnegative real numbers.

Thus, the given random variable is a continuous random variable.

d.

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a discrete random variable.

Explanation of Solution

Given info:

The number of points scored by the Miami Heat in a randomly selected basketball game

Justification:

Denote the random variable X as “number of points scored by the Miami Heat in a randomly selected basketball game”. This is a discrete random variable because the value of the random variable is obtained from counting. That is, there can be 0,1,2,... number of points scored by the Miami Heat in a randomly selected basketball game. Hence, the possible values of the random variable X are x = 0, 1, 2, 3.... and they are all nonnegative integers.

Thus, the given random variable is a discrete random variable.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

(a)

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a discrete random variable.

Explanation of Solution

Given info:

The number of students in a randomly selected elementary school class room.

Justification:

Random Variable:

A random variable X is a numerical outcome of a probability experiment. Moreover, there is a numerical value which is determined by chance for each outcome in the procedure or experiment.

Discrete random variable:

A discrete random variable takes a collection of values which is finite or countable.

Denote the random variable X as “number of students in a randomly selected elementary school class room”. This is a discrete random variable because the value of the random variable is obtained from counting. That is, there can be 0,1,2,... the number of students in a randomly selected elementary school class room. Hence the possible values of the random variable X are x = 0, 1, 2, 3.... and they are all nonnegative integers.

Thus, the given random variable is a discrete random variable.

b.

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a continuous random variable.

Explanation of Solution

Given info:

The variable is “The amount of snow that falls in Minneapolis during the winter season”.

Justification:

Continuous random variable:

A continuous random variable takes infinitely many values or a collection of values which is uncountable. It is impossible to count the items as they are measured in a continuous scale.

Denote the random variable S as “The amount of snow that falls in Minneapolis during the winter season”. Here, the amount of snow that falls in Minneapolis during the winter season measured and it is a continuous random variable. Hence, the possible values of the random variable S are all positive real numbers.

So, the given random variable is a continuous random variable.

c.

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a continuous random variable.

Explanation of Solution

Given info:

The flight time accumulated by a randomly selected Air Force fighter pilot

Justification:

Denote the random variable T as “The flight time accumulated by a randomly selected Air Force fighter pilot”. This is a continuous random variable because the value of the random variable is obtained from a measurement. Hence, the possible values of the random variable T are all nonnegative real numbers.

Thus, the given random variable is a continuous random variable.

d.

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a discrete random variable.

Explanation of Solution

Given info:

The number of points scored by the Miami Heat in a randomly selected basketball game

Justification:

Denote the random variable X as “number of points scored by the Miami Heat in a randomly selected basketball game”. This is a discrete random variable because the value of the random variable is obtained from counting. That is, there can be 0,1,2,... number of points scored by the Miami Heat in a randomly selected basketball game. Hence, the possible values of the random variable X are x = 0, 1, 2, 3.... and they are all nonnegative integers.

Thus, the given random variable is a discrete random variable.

Answer 8

(a)

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a discrete random variable.

Explanation of Solution

Given info:

The number of students in a randomly selected elementary school class room.

Justification:

Random Variable:

A random variable X is a numerical outcome of a probability experiment. Moreover, there is a numerical value which is determined by chance for each outcome in the procedure or experiment.

Discrete random variable:

A discrete random variable takes a collection of values which is finite or countable.

Denote the random variable X as “number of students in a randomly selected elementary school class room”. This is a discrete random variable because the value of the random variable is obtained from counting. That is, there can be 0,1,2,... the number of students in a randomly selected elementary school class room. Hence the possible values of the random variable X are x = 0, 1, 2, 3.... and they are all nonnegative integers.

Thus, the given random variable is a discrete random variable.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer 13

Answer to Problem 1RE

The given random variable is a discrete random variable.

Answer 14

Explanation of Solution

Given info:

The number of students in a randomly selected elementary school class room.

Justification:

Random Variable:

A random variable X is a numerical outcome of a probability experiment. Moreover, there is a numerical value which is determined by chance for each outcome in the procedure or experiment.

Discrete random variable:

A discrete random variable takes a collection of values which is finite or countable.

Denote the random variable X as “number of students in a randomly selected elementary school class room”. This is a discrete random variable because the value of the random variable is obtained from counting. That is, there can be 0,1,2,... the number of students in a randomly selected elementary school class room. Hence the possible values of the random variable X are x = 0, 1, 2, 3.... and they are all nonnegative integers.

Thus, the given random variable is a discrete random variable.

Answer 15

b.

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a continuous random variable.

Explanation of Solution

Given info:

The variable is “The amount of snow that falls in Minneapolis during the winter season”.

Justification:

Continuous random variable:

A continuous random variable takes infinitely many values or a collection of values which is uncountable. It is impossible to count the items as they are measured in a continuous scale.

Denote the random variable S as “The amount of snow that falls in Minneapolis during the winter season”. Here, the amount of snow that falls in Minneapolis during the winter season measured and it is a continuous random variable. Hence, the possible values of the random variable S are all positive real numbers.

So, the given random variable is a continuous random variable.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer 20

Answer to Problem 1RE

The given random variable is a continuous random variable.

Answer 21

Explanation of Solution

Given info:

The variable is “The amount of snow that falls in Minneapolis during the winter season”.

Justification:

Continuous random variable:

A continuous random variable takes infinitely many values or a collection of values which is uncountable. It is impossible to count the items as they are measured in a continuous scale.

Denote the random variable S as “The amount of snow that falls in Minneapolis during the winter season”. Here, the amount of snow that falls in Minneapolis during the winter season measured and it is a continuous random variable. Hence, the possible values of the random variable S are all positive real numbers.

So, the given random variable is a continuous random variable.

Answer 22

c.

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a continuous random variable.

Explanation of Solution

Given info:

The flight time accumulated by a randomly selected Air Force fighter pilot

Justification:

Denote the random variable T as “The flight time accumulated by a randomly selected Air Force fighter pilot”. This is a continuous random variable because the value of the random variable is obtained from a measurement. Hence, the possible values of the random variable T are all nonnegative real numbers.

Thus, the given random variable is a continuous random variable.

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer 27

Answer to Problem 1RE

The given random variable is a continuous random variable.

Answer 28

Explanation of Solution

Given info:

The flight time accumulated by a randomly selected Air Force fighter pilot

Justification:

Denote the random variable T as “The flight time accumulated by a randomly selected Air Force fighter pilot”. This is a continuous random variable because the value of the random variable is obtained from a measurement. Hence, the possible values of the random variable T are all nonnegative real numbers.

Thus, the given random variable is a continuous random variable.

Answer 29

d.

Expert Solution

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer to Problem 1RE

The given random variable is a discrete random variable.

Explanation of Solution

Given info:

The number of points scored by the Miami Heat in a randomly selected basketball game

Justification:

Denote the random variable X as “number of points scored by the Miami Heat in a randomly selected basketball game”. This is a discrete random variable because the value of the random variable is obtained from counting. That is, there can be 0,1,2,... number of points scored by the Miami Heat in a randomly selected basketball game. Hence, the possible values of the random variable X are x = 0, 1, 2, 3.... and they are all nonnegative integers.

Thus, the given random variable is a discrete random variable.

Answer 30

d.

Expert Solution

Answer 31

d.

Expert Solution

Answer 32

Expert Solution

Answer 33

To determine

Whether the random variable is discrete or continuous and to state the possible values of the random variable.

Answer 34

Answer to Problem 1RE

The given random variable is a discrete random variable.

Answer 35

Explanation of Solution

Given info:

The number of points scored by the Miami Heat in a randomly selected basketball game

Justification:

Denote the random variable X as “number of points scored by the Miami Heat in a randomly selected basketball game”. This is a discrete random variable because the value of the random variable is obtained from counting. That is, there can be 0,1,2,... number of points scored by the Miami Heat in a randomly selected basketball game. Hence, the possible values of the random variable X are x = 0, 1, 2, 3.... and they are all nonnegative integers.

Thus, the given random variable is a discrete random variable.