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CAIE A-Level Mathematics 5.4.1 Discrete Random Variables

Practise deriving a probability distribution table from an experiment and using its values to calculate expectation, second moments and variance for a discrete random variable.

Syllabus
2028–2030
Course
Mathematics 9709
Level
AS

Exam points

  • enumerate the possible values of X and attach the probability of every corresponding outcome
  • check that all table probabilities sum to one before calculating any moment or parameter
  • evaluate E(X) and E(X²), then calculate Var(X) = E(X²) − [E(X)]² from those moments

5.4.1—Discrete random variables question 1

[Maximum number: 3]

An ordinary fair die is thrown repeatedly until a 1 or a 6 is obtained.

On another occasion, this die is thrown 3 times. The random variable X is the number of times that a 1 or a 6 is obtained.

On another occasion, this die is thrown 3 times. The random variable X is the number of times that a 1 or a 6 is obtained.

Draw up the probability distribution table for X.

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