CAIE S2 2022 June — Question 4

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2022
SessionJune
TopicLinear combinations of normal random variables
TypePure expectation and variance calculation
4 The independent random variables \(X\) and \(Y\) have distributions \(\operatorname { Po } ( 2 )\) and \(\mathrm { B } \left( 20 , \frac { 1 } { 4 } \right)\) respectively.
  1. Find the mean and standard deviation of \(X - 3 Y\).
  2. Find \(\mathrm { P } ( Y = 15 X )\).
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