Grade 9 Exam > Grade 9 Notes > Statistics & Probability > Worksheet (with Solutions): Transforming & Combining Random Variables
Worksheet (with Solutions): Transforming & Combining Random Variables
# Transforming & Combining Random Variables ## Grade 9 Statistics & Probability Worksheet
Section A: Multiple Choice Questions
Q1: If X is a random variable with mean μX = 10 and standard deviation σX = 3, what is the mean of Y = 2X + 5?
(a) 15
(b) 20
(c) 25
(d) 30
Q2: A random variable X has a standard deviation of 4. If Y = 3X, what is the standard deviation of Y?
(a) 4
(b) 7
(c) 12
(d) 16
Q3: If X and Y are independent random variables with variances Var(X) = 9 and Var(Y) = 16, what is Var(X + Y)?
(a) 5
(b) 7
(c) 25
(d) 144
Q4: Random variable X has mean 50 and standard deviation 5. What is the variance of W = X - 10?
(a) 5
(b) 15
(c) 25
(d) 40
Q5: If X and Y are independent with means μX = 8 and μY = 12, what is the mean of X - Y?
(a) -4
(b) 4
(c) 20
(d) 96
Q6: If X has Var(X) = 20 and Y has Var(Y) = 15, and X and Y are independent, what is Var(X - Y)?
(a) 5
(b) 15
(c) 25
(d) 35
Q7: A random variable X has mean 100 and variance 36. What is the standard deviation of Z = -2X + 50?
(a) 6
(b) 12
(c) 36
(d) 72
Q8: Three independent random variables X, Y, and Z have variances 4, 9, and 5 respectively. What is Var(X + Y + Z)?
(a) 6
(b) 18
(c) 36
(d) 180
Section B: Fill in the Blanks
Q9: When a constant is added to a random variable, the mean increases by that constant but the __________ remains unchanged.Q10: If X and Y are independent random variables, then Var(X + Y) = Var(X) + __________.Q11: For a linear transformation Y = aX + b, the variance of Y is given by Var(Y) = __________ × Var(X).Q12: If two random variables X and Y are independent, then the variance of their difference Var(X - Y) = Var(X) + Var(Y), which means variances __________ for both sums and differences.Q13: The expected value (mean) of the sum of two random variables equals the __________ of their individual expected values, regardless of whether they are independent.Q14: If the standard deviation of X is σX, then the standard deviation of 5X is __________.Section C: Word Problems
Q15: A coffee shop sells cups of coffee with a mean volume of 350 mL and a standard deviation of 8 mL. If each cup is measured and then 50 mL of cream is added, what are the new mean and standard deviation of the total volume?Q16: The time spent on homework for math has a mean of 45 minutes with a standard deviation of 10 minutes. The time spent on science homework has a mean of 30 minutes with a standard deviation of 8 minutes. Assuming the times are independent, find the mean and standard deviation of the total homework time.Q17: A store marks up the wholesale price of an item by tripling it and then adding $15. If the wholesale price has a mean of $40 and a standard deviation of $5, what are the mean and standard deviation of the retail price?Q18: Two independent random variables X and Y have the following properties: X has mean 20 and variance 25, while Y has mean 15 and variance 16. Calculate the mean and variance of the random variable D = X - Y.Q19: A factory produces bolts with lengths that have a mean of 50 mm and a standard deviation of 0.5 mm. Quality control requires that each bolt length be measured and then converted to centimeters by dividing by 10. What are the mean and standard deviation of the bolt lengths in centimeters?Q20: A student takes three independent quizzes. Quiz 1 has a mean score of 80 with variance 9, Quiz 2 has a mean of 75 with variance 16, and Quiz 3 has a mean of 85 with variance 4. If the total score T is the sum of all three quiz scores, find the mean and standard deviation of T.The document Worksheet (with Solutions): Transforming & Combining Random Variables is a part of the Grade 9 Course Statistics & Probability.
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Apr 20, 2026 Last updated
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