Chapter 6, Problem 1RE

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

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

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.

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.

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.

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.