Question

determine whether the statement is true or false. if it is false, rewrite it as a true statement.

for a random variable \\(x\\), the word random indicates that the value of \\(x\\) is determined by chance.

choose the correct answer below.

a. the statement is false. random indicates any variable can be used, not necessarily \\(x\\).
b. the statement is false. random indicates that the variable has an uncountable number of possible outcomes, represented by an interval on a number line.
c. true.
d. the statement is false. random indicates that the variable has a finite or countable number of possible outcomes that can be listed.

Explanation:

Analyze the definition of a random variable

A random variable is a numerical description of the outcome of a statistical experiment. The term "random" signifies that the specific value the variable takes on is determined by chance or a random process.

Evaluate the given statement

The statement is: "For a random variable \(x\), the word random indicates that the value of \(x\) is determined by chance." This aligns perfectly with the fundamental definition of a random variable, making the statement true.

Match with the multiple-choice options

Option C is "True", which matches the evaluation.

Answer:

• A. The statement is false. Random indicates any variable can be used, not necessarily x.
• B. The statement is false. Random indicates that the variable has an uncountable number of possible outcomes, represented by an interval on a number line.
• C. True. (Correct answer)
• D. The statement is false. Random indicates that the variable has a finite or countable number of possible outcomes that can be listed.