CAIE A-Level Mathematics 6.2 Linear Combinations of Random Variables
Practise forming distributions for sums, differences and scaled independent normal variables before calculating probabilities.
- Syllabus
- 2028–2030
- Course
- Mathematics 9709
- Level
- A2
Exam points
- combine means linearly but add squared-coefficient variances for independent variables
- translate a contextual comparison into one linear combination before standardising
- use the derived mean and standard deviation to calculate the required probability
Covered syllabus points
6.2 Linear combinations of random variables question 1
[Maximum number: 3]
The number, X, of books received at a charity shop has a constant mean of 5.1 per day.
Find the probability that the total number of books and DVDs that are received at the shop in 1 day is more than 3 .
(=) 5.1+2.5 [=7.6]
B1
Give at early stage (seen or implied).
1-e^-7.6(1+7.6+7.6^22+7.6^33!)=1-e^-7.6(1+7.6+28.88+73.16) =1-(0.0005005+0.003803+0.01445+0.03661)1-e^-7.6(1+7.6+7.6^22+7.6^33!)=1-e^-7.6(1+7.6+28.88+73.16)=1-(0.0005005+0.003803+0.01445+0.03661)
M1
Allow incorrect . Allow one end error.
Must see an expression (accept correct sigma notation).
=0.945(3 sf)
A1
SC No working, 0.945 B1(could be implied) SC B1.
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