CAIE A-Level Mathematics 6.2.1 Linear Combinations of Random Variables

CAIE A-Level Mathematics 6.2.1 Linear Combinations of Random Variables
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise finding the distribution of aX + bY from independent normal or Poisson variables, transforming means linearly and adding variance contributions with squared coefficients.

How this is tested

  • calculate E(aX + bY) as aE(X) + bE(Y), retaining the sign of each coefficient
  • calculate variance as a²Var(X) + b²Var(Y) for independent variables, even for differences
  • state the resulting normal or Poisson model before standardising the required sum or comparison

Question 6

[Maximum number: 10]

The masses, in kilograms, of large and small bags of potatoes have the independent distributions N(2.5,0.05) and N(0.8,0.02) respectively.

Question 6(a)

(a)

Find the probability that the total mass of a randomly chosen large bag of potatoes and a randomly chosen small bag of potatoes is more than 3.55 kg .

[ 5 ]

Question 6(b)

(b)

Find the probability that the mass of a randomly chosen large bag of potatoes is less than 3 times the mass of a randomly chosen small bag of potatoes.

[ 5 ]