SA4-SA5 Expectation and linear functions Quiz: AQA Further Maths, Unit 4

The 20 questions

1. For a discrete random variable X, which expression gives the expectation E(X)?

   • Sum of x_i divided by n
   • Sum of x_i p_i
   • Sum of p_i
   • Sum of x_i squared p_i

2. Which expression gives E(X^2) for a discrete random variable X?

   • Sum of x_i squared p_i
   • Sum of x_i squared
   • Sum of x_i p_i all squared
   • Sum of x_i p_i squared

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

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

4. For constants a and b, which expression gives E(aX + b)?

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

5. For constants a and b, which expression gives Var(aX + b)?

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

6. For a function g of a discrete random variable X, which expression gives E(g(X))?

   • g(E(X))
   • Sum of x_i g(p_i)
   • Sum of g(x_i) p_i
   • Sum of g(x_i) divided by n

7. What is the expectation of a constant c?

   • c
   • c divided by 2
   • 0
   • c squared

8. A discrete random variable X takes values 1, 2 and 3 with probabilities 0.2, 0.5 and 0.3. What is E(X)?

   • 2
   • 2.1
   • 2.5
   • 1.9

9. For the same variable X taking values 1, 2 and 3 with probabilities 0.2, 0.5 and 0.3, what is E(X^2)?

   • 4.9
   • 2.1
   • 4.41
   • 6.0

10. For the same variable X taking values 1, 2 and 3 with probabilities 0.2, 0.5 and 0.3, what is Var(X)?

    • 4.41
    • 4.9
    • 0.7
    • 0.49

11. For the same variable X, let Y = 3X + 2. What is E(Y)?

    • 8.3
    • 6.3
    • 11.6
    • 4.1

12. For the same variable X, let Y = 3X + 2. What is Var(Y)?

    • 4.41
    • 0.49
    • 1.47
    • 2.94

13. For the same variable X taking values 1, 2 and 3 with probabilities 0.2, 0.5 and 0.3, what is E(X^3)?

    • 8.3
    • 9.26
    • 12.3
    • 4.9

14. A random variable X has E(X) = 4 and Var(X) = 3. What is E(2X - 5)?

    • 13
    • -3
    • 8
    • 3

15. A random variable X has E(X) = 4 and Var(X) = 3. What is Var(2X - 5)?

    • 24
    • 6
    • 3
    • 12

16. A discrete random variable X has E(X) = 2 and E(X^2) = 10. What is Var(X)?

    • 6
    • 8
    • 10
    • 4

17. Two independent random variables X and Y have Var(X) = 2 and Var(Y) = 3. What is Var(X + Y)?

    • 2.5
    • 6
    • 5
    • 1

18. A discrete random variable has P(X = x) = x/6 for x = 1, 2, 3. What is E(X)?

    • 3
    • 7/3
    • 2
    • 14/3

19. A random variable X has E(X) = 3 and Var(X) = 4. Y = aX + b has E(Y) = 0 and Var(Y) = 16, with a > 0. What are a and b?

    • a = 2, b = 6
    • a = 4, b = -6
    • a = 2, b = -6
    • a = -2, b = 6

20. A discrete random variable X takes values -1, 0 and 1 with probabilities 0.25, 0.5 and 0.25. What is Var(X)?

    • 0.25
    • 0.5
    • 1
    • 0

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