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mean and standard deviation of random variables

Review mean and standard deviation of random variables for AP Statistics and try 2 free AP-style practice questions. 9 questions on this topic in AP Statistics · Unit 4 · Probability, Random Variables, and Probability Distributions.

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Question 1

A shop's daily revenue XX and daily cost YY are independent random variables with E(X)=5,000E(X) = 5{,}000 dollars, E(Y)=3,200E(Y) = 3{,}200 dollars, Var(X)=640,000\text{Var}(X) = 640{,}000 and Var(Y)=250,000\text{Var}(Y) = 250{,}000. Daily profit is X−YX - Y. Which of the following gives the expected daily profit and its standard deviation?

Question 2

A basketball player takes 2 free throws. The probability that she makes the first is 0.75. If she makes the first, the probability that she makes the second is 0.80; if she misses the first, the probability that she makes the second is 0.60. Let XX be the number of free throws she makes. Which of the following gives the mean and the variance of XX?

7 more questions on this topic

Full practice for AP Statistics · Unit 4 · Probability, Random Variables, and Probability Distributions: timed tests, step-by-step explanations for every answer, and AI grading for free-response questions.

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Answer, then see why

The price of gasoline rises 10% and the quantity demanded falls 5%. What happens to total revenue?

Not quite. The answer is B.

Why the other options are wrong

AI grading for free-response

Write your FRQ answer and get it scored point by point against the AP rubric, with the line from your answer that earned or missed each point.

Question 13 / 4 pts
Part a1 / 1 pts
Point 1: Earned
Grader confidence 94% sure

Reason: Correctly identifies demand for gasoline as inelastic.

Evidence: "The price of gasoline rises and the quantity falls only a little."

Part b2 / 3 pts
Point 1: Earned
Grader confidence 91% sure

Reason: Graph shows relatively inelastic demand.

Evidence: Draws a steep demand curve.

Point 2: Earned
Grader confidence 88% sure

Reason: Correct new equilibrium price.

Evidence: Shifts supply left, P1 → P2.

Point 3: Not earned
Grader confidence 82% sure

Reason: With inelastic demand, a price increase raises total revenue.

Evidence: "Revenue goes down."

Mean and standard deviation of random variables: AP Statistics Practice Questions | S&D Academy