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

The 20 questions

1. A discrete random variable is one that:

   • Has a probability density function
   • Can only take positive whole numbers
   • Takes a countable set of values, each with a probability
   • Takes any value in an interval of the real line

2. For a probability distribution of a discrete random variable X, what must the probabilities P(X = x) sum to?

   • 0
   • The number of values taken
   • 0.5
   • 1

3. The mode of a discrete random variable is:

   • The average of the values
   • The smallest value taken
   • The middle value when the values are ordered
   • The value with the highest probability

4. The median of a discrete random variable X is a value m such that:

   • m is the largest value taken
   • P(X <= m) equals 1
   • P(X = m) equals 0.5
   • P(X <= m) is at least 0.5 and P(X >= m) is at least 0.5

5. Which pair of conditions must the function p(x) = P(X = x) satisfy to be a valid probability function?

   • p(x) must be greater than 1 for every value
   • 0 <= p(x) <= 1 and the sum of p(x) is 1
   • The sum of p(x) is 0
   • p(x) can be negative provided the sum is 1

6. The standard deviation of a discrete random variable is:

   • The positive square root of the variance
   • The variance divided by the mean
   • The variance squared
   • The mean squared

7. How is the cumulative probability P(X <= x) for a discrete random variable found from its probability table?

   • Multiplying all the probabilities up to x
   • Taking the probability at x alone
   • Summing the probabilities of all values up to and including x
   • Averaging the probabilities of all values

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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