Edexcel International A Level Maths: Statistics 1

Revision Notes

3.1.3 aX+b

Test Yourself


How are the mean and variance of X related to the mean and variance of aX + b?

  • If a and b are constants then the following results are true
    • E(aX + b) = aE(X) + b
    • Var(aX + b) = a² Var(X)
  • Note that the mean is affected by multiplication and addition whereas addition does not change the variance
  • The factor of   includes the squared because the values of X are squared in the calculation
    • You could try and use the first result and the formula for variance to verify the second result
  • Remember a subtraction can be written as an addition
    • X – b can be written as X + (-b)
  • And division can be written as a multiplication
    • begin mathsize 16px style x over a end stylecan be written as begin mathsize 16px style 1 over a X end style

Worked example

X is a random variable such that E left parenthesis X right parenthesis equals 5 and Var left parenthesis X right parenthesis equals 4.

Find the value of:

straight E left parenthesis 3 X plus 5 right parenthesis
Var left parenthesis 3 X plus 5 right parenthesis
Var left parenthesis 2 minus X right parenthesis


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Author: Dan

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.