5.02a-c Discrete random variables, expectation and variance Quiz: OCR Further Maths, Unit 2

The 20 questions

1. What is the sum of all probabilities in a discrete probability distribution?

   • 0.5
   • 0
   • Infinity
   • 1

2. Which expression defines the expectation E(X) for a discrete random variable X?

   • Σ P(X=x)
   • Σ x P(X=x)
   • Σ x
   • Σ x^2 P(X=x)

3. Which formula gives the variance Var(X) of a discrete random variable X?

   • [E(X)]^2 - E(X^2)
   • E(X^2) + [E(X)]^2
   • E(X) - E(X^2)
   • E(X^2) - [E(X)]^2

4. What is the expectation E(aX + b) for constants a and b?

   • E(X) + b
   • a E(X)
   • a E(X) + a b
   • a E(X) + b

5. What is the variance Var(aX + b) for constants a and b?

   • a^2 Var(X) + b
   • a Var(X) + b
   • a Var(X)
   • a^2 Var(X)

6. What does the cumulative distribution function F(x) represent for a random variable X?

   • P(X = x)
   • P(X >= x)
   • P(X > x)
   • P(X <= x)

7. What is the variance of a constant c, denoted Var(c)?

   • 0
   • c
   • c^2
   • 1

8. For independent random variables X and Y, what is Var(X - Y)?

   • Var(X) - Var(Y)
   • Var(X) Var(Y)
   • a^2 Var(X)
   • Var(X) + Var(Y)

9. If P(X=1) = 0.3 and P(X=2) = 0.7, what is E(X)?

   • 1.7
   • 1.5
   • 0.7
   • 1.3

10. If X takes values 0 and 1 with equal probability 0.5, what is Var(X)?

    • 0.125
    • 0.75
    • 0.25
    • 0.5

11. If E(X) = 4, what is the value of E(3X - 2)?

    • 12
    • 10.5
    • 10
    • 14

12. If Var(X) = 5, what is the value of Var(2X + 3)?

    • 10
    • 13
    • 20
    • 23

13. A random variable X has P(X=x) = k x for x = 1, 2, 3. What is k?

    • 1/3
    • 1/6
    • 1/2
    • 1/4

14. If E(X) = 3 and E(X^2) = 13, what is Var(X)?

    • 16
    • 4
    • 10
    • 7

15. For a random variable X taking values 2 and 4, if F(2) = 0.4, what is P(X = 4)?

    • 0.2
    • 0.4
    • 0.6
    • 0.8

16. If X and Y are independent with Var(X) = 3 and Var(Y) = 4, find Var(X + Y).

    • 12
    • 1
    • 25
    • 7

17. If X takes values -1, 0, 1 with equal probability 1/3, what is E(X^3)?

    • 0
    • 1/3
    • -1/3
    • 2/3

18. If Var(X) = 3, what is the exact value of Var(-3X + 5)?

    • 9
    • 27
    • -27
    • -9

19. A discrete uniform variable X takes integer values from 1 to 5 inclusive. What is Var(X)?

    • 2
    • 2.5
    • 3
    • 1.5

20. If X and Y are independent with Var(X) = 2 and Var(Y) = 3, what is Var(3X - 2Y)?

    • 6
    • 12
    • 18
    • 30

Related quizzes

• Probability by calculation and conditional probability Quiz · 5.01a · 20 questions
• Binomial and discrete uniform distributions Quiz · 5.02d-e · 20 questions
• Geometric and Poisson distributions Quiz · 5.02f-i · 20 questions
• Continuous random variables and probability density functions Quiz · 5.03a-d · 20 questions
• Cumulative distribution functions Quiz · 5.03e · 20 questions
• Linear combinations of random variables Quiz · 5.04a-b · 20 questions
• Sampling distributions and unbiased estimates Quiz · 5.05a-b · 20 questions
• Normal-based hypothesis tests and confidence intervals Quiz · 5.05c-d · 20 questions
• Chi-squared tests on contingency tables Quiz · 5.06a · 20 questions
• Goodness of fit and fitting theoretical distributions Quiz · 5.06b-d · 20 questions