Concept explainers
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)
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.
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.
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.
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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