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CAIE A Level Mathematics 9709

Discrete random variables questions

Exam-style questions on Discrete random variables, ordered from foundation to challenge. Pick one, write your answer the way you would in the exam, and it comes back marked against the mark scheme, point by point.

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Written by Markquill to follow the Cambridge International syllabus. Markquill is independent and is not affiliated with or endorsed by Cambridge International.

  1. 2 marksFoundationThe discrete random variable X has the following probability distribution: x 1 2 3 4 P(X = x) frac110 frac410 frac410 p Given that the probabilities sum to 1, find the value of p.
  2. 2 marksFoundationThe discrete random variable X has the following probability distribution, where p is an unknown probability: x 1 2 3 P(X = x) 1/10 2/10 p Find the value of p.
  3. 2 marksFoundationA factory produces light bulbs. The probability that a bulb is defective is 0.25. A quality inspector selects a random sample of 20 bulbs. Let X be the number of defective bulbs in the sample.
  4. 2 marksFoundationA machine produces components independently, and each component is faulty with probability 40\%. A sample of 100 components is taken, and X is the number of faulty components in the sample.
  5. 3 marksStandardThe discrete random variable X has the following probability distribution: x 4 3 7 P(X=x) 1/10 4/10 5/10 Find E(X).
  6. 3 marksStandardEach time a machine is switched on it starts correctly with probability 60\%, independently of every other attempt. The random variable X is the number of the attempt on which it first starts correctly.
  7. 3 marksStandardA binomial experiment consists of 2 independent trials, each with probability of success 0.2. Find the probability of at least one success.
  8. 4 marksStandardThe discrete random variable X has the probability distribution shown. x 1 3 6 P(X = x) 0.4 0.5 0.1
  9. 2 marksChallengeA discrete random variable X has Var(X) = 1.2. A second variable is defined by Y = -4X - 3.
  10. 2 marksChallengeA discrete random variable X has E(X) = 2. A second variable is defined by Y = 5X - 6.
  11. 3 marksChallengeEach time a machine is switched on it starts correctly with probability 90\%, independently of every other attempt. The random variable X is the number of the attempt on which it first starts correctly.