3B.1.1 Expectation of discrete random variables Quiz: Pearson Edexcel Further Maths, Unit 10

The 20 questions

1. What is the formula for the expectation E(X) of a discrete random variable X?

   • E(X) = sum of P(X = x)
   • E(X) = sum of P(X = x) / x
   • E(X) = sum of x P(X = x)
   • E(X) = sum of x^2 P(X = x)

2. Which expression is equivalent to Var(X) for a discrete random variable?

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

3. What is E(aX + b) in terms of E(X)?

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

4. What is Var(aX + b) in terms of Var(X)?

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

5. A random variable has P(X = 0) = 0.1, P(X = 1) = 0.3, P(X = 2) = 0.4 and P(X = 3) = 0.2. What is E(X)?

   • 2.0
   • 1.9
   • 1.7
   • 1.5

6. For the same distribution (P(X=0)=0.1, P(X=1)=0.3, P(X=2)=0.4, P(X=3)=0.2), what is Var(X)?

   • 0.61
   • 1.21
   • 0.81
   • 0.89

7. A fair six-sided die is rolled once. What is E(X)?

   • 4
   • 3.5
   • 3.25
   • 3

8. For a fair six-sided die, what is Var(X)?

   • 2.5
   • 35/12
   • 91/6
   • 35/6

9. If E(X) = 3, what is E(2X + 1)?

   • 6
   • 4
   • 7
   • 9

10. If Var(X) = 4, what is Var(3X - 2)?

    • 10
    • 6
    • 36
    • 12

11. If E(X) = 2 and Var(X) = 5, what is E(X^2)?

    • 9
    • 4
    • 7
    • 5

12. A game pays 5 pounds with probability 0.2 and costs 1 pound with probability 0.8. What is the expected payoff?

    • 0.20 pounds
    • -0.20 pounds
    • 0.80 pounds
    • 1.00 pounds

13. A random variable has P(X = x) = kx for x = 1, 2, 3, 4 and zero otherwise. What is k?

    • 0.25
    • 0.2
    • 0.4
    • 0.1

14. Using the same distribution P(X = x) = 0.1x for x = 1, 2, 3, 4, what is E(X)?

    • 2
    • 3.5
    • 2.5
    • 3

15. If E(X) = 2 and Var(X) = 1, what is E((X - 2)^2)?

    • 1
    • 0
    • 4
    • 5

16. If E(X) = 4 and E(X^2) = 20, what is Var(X)?

    • 24
    • 4
    • 16
    • 20

17. A random variable takes the values 1 and 3, each with probability 0.5. What is E(X)?

    • 1.5
    • 3
    • 2.5
    • 2

18. A fair coin is tossed three times and X is the number of heads. What is E(X)?

    • 2
    • 1.5
    • 3
    • 1

19. A discrete random variable has E(X) = 5 and Var(X) = 3. What is E(X^2)?

    • 8
    • 3
    • 28
    • 25

20. Which statement about E(g(X)) for a discrete random variable is correct?

    • E(g(X)) = g(E(X)) always
    • E(g(X)) = sum of g(P(X = x))
    • E(g(X)) = sum of x P(X = x) multiplied by g
    • E(g(X)) = sum of g(x) P(X = x)

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