CAIE S2 2024 June — Question 4

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2024
SessionJune
TopicLinear combinations of normal random variables
TypeDirect comparison of two variables

4 A random variable \(X\) has the distribution \(\mathrm { N } ( 10,12 )\). Two independent values of \(X\), denoted by \(X _ { 1 }\) and \(X _ { 2 }\), are chosen at random.
  1. Write down the value of \(\mathrm { P } \left( X _ { 1 } > X _ { 2 } \right)\).
  2. Find \(\mathrm { P } \left( X _ { 1 } > 2 X _ { 2 } - 3 \right)\).