AP Statistics Random Variables, Expected Value and Combining Variables Quiz: 10 Questions with Explanations

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This random variables quiz for AP Statistics covers random variables, expected value and combining variables (Common Core AP STAT 4.7, AP STAT 4.8, AP STAT 4.9, HSS-MD.A.1, HSS-MD.A.2, HSS-MD.B.5), with a free PDF to print.

Ten multiple-choice questions check the rules for means and standard deviations of random variables. Read each explanation, since adding standard deviations is the most common error.

AP Statistics · Common Core State Standards: AP STAT 4.7, AP STAT 4.8, AP STAT 4.9, HSS-MD.A.1, HSS-MD.A.2, HSS-MD.B.5

Random variables quiz: 10 questions

Question 1
x012P(x)0.50.30.2
Distribution of X.

What is the mean of X?

Question 2
00.10.20.30.40.5Probability0.110.220.330.44x
Histogram of Y.

What is E(Y)?

Question 3
VariableMeanSDX103Y64
Independent variables.

What is the standard deviation of X + Y?

Question 4
VariableMeanSDX103Y64
Independent variables.

What is the mean of X – Y?

Question 5
If Y = 4X + 1, and X has standard deviation 2, the standard deviation of Y is:

Question 6
A fair game has expected net gain of:

Question 7
Which probabilities could define a distribution?

Question 8
Independent X, Y have sd 5 and 12. The sd of X – Y is:

Question 9
The expected value of a random variable is best interpreted as:

Question 10
If the weights of two independent items have means 3 and 5 lb, the mean total weight is:

Remember

Remember
  • Probabilities in a distribution are between 0 and 1 and sum to 1.
  • Mean (expected value): sum of x p; interpret it as the long-run average.
  • Standard deviation: square root of the sum of (x – mean)^2 p.
  • For a + bX: mean a + b mu, standard deviation |b| sigma.
  • For independent X, Y: means add or subtract; variances add (also for X – Y).

How to use this random variables quiz

Answer each question, read the explanation that appears, and keep track of your score. A score of 8 out of 10 or more means you are ready for the test.

Download the random variables quiz as a PDF with the button below and keep it with your notes.

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AP Statistics Random Variables, Expected Value and Combining Variables Quiz: 10 Questions with Explanations

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