Edexcel S3 2003 June — Question 3

Exam BoardEdexcel
ModuleS3 (Statistics 3)
Year2003
SessionJune
TopicLinear combinations of normal random variables
TypeTwo or more different variables
3. Given the random variables \(X \sim \mathrm {~N} ( 20,5 )\) and \(Y \sim \mathrm {~N} ( 10,4 )\) where \(X\) and \(Y\) are independent, find
  1. \(\mathrm { E } ( X - Y )\),
  2. \(\operatorname { Var } ( X - Y )\),
  3. \(\mathrm { P } ( 13 < X - Y < 16 )\).
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