CAIE A-Level Mathematics 5.4.1 Discrete Random Variables

CAIE A-Level Mathematics 5.4.1 Discrete Random Variables
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

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.

How this is tested

  • 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

Question 1

[Maximum number: 4]

The random variable X takes the value x with probability kx2k x^{2}, where k is a constant and x takes the values -2,1,2,3 only.

Question 1(a)

(a)

Draw up the probability distribution table for X, giving the probabilities as numerical fractions.

[ 3 ]

Question 1(b)

(b)

Find E(X).

[ 1 ]