SPS SPS FM Statistics 2020 October — Question 2

Exam BoardSPS
ModuleSPS FM Statistics (SPS FM Statistics)
Year2020
SessionOctober
TopicLinear combinations of normal random variables
TypePure expectation and variance calculation

2. The independent random variables \(X\) and \(Y\) are such that \(\mathrm { E } ( X ) = 20 , \mathrm { E } ( Y ) = 10\), \(\operatorname { Var } ( X ) = 5\) and \(\operatorname { Var } ( Y ) = 4\). Find:
a. \(\mathrm { E } ( 2 X - Y )\)
b. \(\operatorname { Var } ( 2 X - Y )\)