Question

what does the mean of a probability distribution represent?

choose the correct answer below.

a. it gives information about how the outcomes vary.
b. it can never be negative.
c. it is the expected value of a discrete random variable.
d. it represents the most likely possible outcome.

Explanation:

Define the mean of a probability distribution

$$ \mu = E(X) = \sum x \cdot P(x) $$

Evaluate the given options

• Option A describes variance or standard deviation, not the mean.
• Option B is incorrect because a random variable can take negative values, making its mean negative.
• Option C correctly identifies that the mean of a probability distribution is the expected value of the random variable.
• Option D describes the mode, not the mean.

Answer:

• A. It gives information about how the outcomes vary.
• B. It can never be negative.
• C. It is the expected value of a discrete random variable. (Correct answer)
• D. It represents the most likely possible outcome.