S4.1.1 Discrete probability distributions Quiz: Pearson Edexcel Maths, Unit 14

The 20 questions

1. What must the sum of all probabilities in a discrete probability distribution always equal?

   • Infinity
   • 0
   • 100
   • 1

2. What condition must every individual probability P(X = x) in a valid distribution satisfy?

   • P(x) >= 0
   • 0 < P(x) < 1
   • 0 <= P(x) <= 1
   • -1 <= P(x) <= 1

3. How is the expectation E(X) of a discrete random variable X generally denoted?

   • Sum of x + P(X = x)
   • Sum of x * P(X = x)
   • Sum of P(X = x) / x
   • Sum of x^2 * P(X = x)

4. What algebraic identity is commonly used to find the variance Var(X)?

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

5. If X is a discrete random variable, what does E(aX + b) equal?

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

6. For constants a and b, what does the variance Var(aX + b) simplify to?

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

7. What is another common name for the expectation E(X) of a random variable?

   • Variance
   • Mode
   • Median
   • Mean

8. Which function is often defined using a probability mass function in discrete distributions?

   • Cumulative distribution function
   • Frequency polygon
   • Normal curve
   • Probability density function

9. A fair six-sided die is rolled. What is the expectation E(X) of the score?

   • 4
   • 6
   • 3.5
   • 3

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

    • 1/6
    • 1/2
    • 1/3
    • 1

11. Find E(X) if X takes values 1 and 2 with probabilities 0.4 and 0.6 respectively.

    • 1.8
    • 1.5
    • 1.2
    • 1.6

12. If Var(X) = 4, what is the variance of the new variable Y = 3X - 2?

    • 10
    • 14
    • 12
    • 36

13. If E(X) = 5 and E(X^2) = 30, what is the variance Var(X)?

    • 5
    • 5.48
    • 25
    • 55

14. A biased coin has P(Head) = 0.6. For 1 Head (score 1) and 0 Heads (score 0), find E(X).

    • 0.5
    • 0.6
    • 1.0
    • 0.4

15. If X has possible values 1, 2, 3 with probabilities 0.2, 0.5, 0.3, what is P(X >= 2)?

    • 0.5
    • 0.2
    • 0.8
    • 0.7

16. A discrete random variable has E(X) = 4. What is E(2X + 3)?

    • 7
    • 8
    • 14
    • 11

17. What does P(X = x) represent for a specific value x in a discrete distribution?

    • Probability mass function
    • Cumulative frequency
    • Probability density function
    • Expected frequency

18. If a discrete distribution has probability function P(X = x) = k/x for x = 1, 2, what is k?

    • 2/3
    • 3/2
    • 1/3
    • 1/2

19. What key property characterises the values taken by a discrete random variable?

    • Continuous interval
    • Countable values
    • Infinite decimals
    • Unbounded range

20. What does a variance of zero imply about a discrete random variable X?

    • It is uniform
    • It is infinite
    • It is constant
    • It is zero

Related quizzes

• Structure of mathematical proof and methods of proof Quiz · 1.1.1 · 20 questions
• Vectors in two and three dimensions Quiz · 10.1.1 · 20 questions
• Laws of indices for all rational exponents Quiz · 2.1.1 · 20 questions
• Straight lines and their equations Quiz · 3.1.1 · 20 questions
• Binomial expansion Quiz · 4.1.1 · 20 questions
• Sine, cosine and tangent for all angles Quiz · 5.1.1 · 20 questions
• Exponential function e^x and its graph Quiz · 6.1.1 · 20 questions
• Derivative as the gradient of a tangent Quiz · 7.1.1 · 20 questions
• Fundamental Theorem of calculus and integration as reverse differentiation Quiz · 8.1.1 · 20 questions
• Locating roots by change of sign Quiz · 9.1.1 · 20 questions