Question

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

the expected value of a random variable can never be negative.

choose the correct answer below.

a. the statement is true.
b. the statement is false. the expected value of a random variable is always 0.
c. the statement is false. the expected value of a random variable is always 1.
d. the statement is false. the expected value of a random variable can be negative.

Explanation:

Analyze the statement

$$ \text{Statement: "The expected value of a random variable can never be negative."} $$

Evaluate the validity and find a counterexample

$$
LATEXBLOCK0
$$

Match with the correct option

$$ \text{The statement is false. The expected value of a random variable can be negative.} \implies \text{Option D} $$

Answer:

• (A) The statement is true.
• (B) The statement is false. The expected value of a random variable is always 0.
• (C) The statement is false. The expected value of a random variable is always 1.
• (D) The statement is false. The expected value of a random variable can be negative. (Correct answer)