CAIE S2 2013 June — Question 1

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2013
SessionJune
TopicDiscrete Random Variables
TypeLinear combinations of independent variables

1 The mean and variance of the random variable \(X\) are 5.8 and 3.1 respectively. The random variable \(S\) is the sum of three independent values of \(X\). The independent random variable \(T\) is defined by \(T = 3 X + 2\).
  1. Find the variance of \(S\).
  2. Find the variance of \(T\).
  3. Find the mean and variance of \(S - T\).