SA1-SA3 Discrete random variables and their measures Quiz: AQA Further Maths, Unit 4

The 20 questions

1. What defining feature characterises a discrete random variable?

   • Negative probability values
   • Infinite smooth spectrum
   • Countable possible values
   • Continuous interval values

2. What is the sum of all probabilities for a discrete random variable?

   • 0
   • Infinity
   • 0.5
   • 1

3. What is the mode of a discrete random variable?

   • Expected mean value
   • Lowest probability value
   • Middle position value
   • Highest probability value

4. For median m of a discrete random variable X, what minimum value must P(X <= m) take?

   • 1
   • 0.25
   • 0
   • 0.5

5. Which pair of conditions defines a valid probability mass function p(x)?

   • p(x) >= 0 and sum is 0
   • 0 <= p(x) <= 1 and sum is 1
   • p(x) <= 0 and sum is 1
   • p(x) >= 1 and sum is 0

6. How is standard deviation calculated from the variance of a discrete random variable?

   • Square root of variance
   • Half of variance
   • Variance squared
   • Square of variance

7. How is the cumulative distribution function F(x) = P(X <= x) evaluated?

   • Integrate density over x
   • Multiply probabilities to x
   • Sum probabilities up to x
   • Subtract x from total probability

8. A discrete random variable X takes values 0, 1, 2, 3 with probabilities 0.1, 0.3, 0.4 and 0.2. What is E(X)?

   • 1.5
   • 1.2
   • 1.7
   • 2

9. For the same variable X taking values 0, 1, 2, 3 with probabilities 0.1, 0.3, 0.4 and 0.2, what is Var(X)?

   • 0.81
   • 0.49
   • 3.7
   • 0.9

10. For the same variable X taking values 0, 1, 2, 3 with probabilities 0.1, 0.3, 0.4 and 0.2, what is P(X >= 2)?

    • 0.4
    • 0.6
    • 0.3
    • 0.7

11. A discrete random variable has P(X = x) = 0.1x for x = 1, 2, 3, 4. What is Var(X)?

    • 10
    • 3.0
    • 2.5
    • 1

12. For the distribution P(X = x) = 0.1x for x = 1, 2, 3, 4, what is the mode?

    • 1
    • 4
    • 3
    • 2.5

13. For the distribution P(X = x) = 0.1x for x = 1, 2, 3, 4, what is the median?

    • 3
    • 2
    • 4
    • 2.5

14. A fair six-sided die is rolled and X is the score. What is Var(X)?

    • 3.5
    • 91/6
    • 35/12
    • 17/12

15. A discrete random variable has P(X = x) = k(x + 1) for x = 0, 1, 2, 3. What is P(X = 3)?

    • 0.1
    • 0.2
    • 0.3
    • 0.4

16. A discrete random variable X takes values 1, 2 and 3 only. P(X = 3) = 0.3 and E(X) = 2.2. What is P(X = 2)?

    • 0.6
    • 0.1
    • 0.5
    • 0.3

17. A discrete random variable X has P(X = 1) = 0.2, P(X = 2) = 0.15, P(X = 3) = 0.35 and P(X = 4) = 0.3. What is its median?

    • 3
    • 2
    • 4
    • 2.5

18. A discrete random variable X takes values 0, 2 and 4 with P(X = 0) = 0.2 and P(X = 2) = 0.6, and E(X) = 2. What is P(X = 4)?

    • 0.1
    • 0.4
    • 0.2
    • 0.6

19. Two fair six-sided dice are rolled and X is the sum of the scores. What is P(X = 7)?

    • 1/12
    • 7/36
    • 1/6
    • 1/36

20. A discrete random variable has P(X = x) = 0.1x for x = 1, 2, 3, 4. What is E(X)?

    • 2.5
    • 3.0
    • 3.5
    • 10

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