OCR S4 2012 June — Question 6

Exam BoardOCR
ModuleS4 (Statistics 4)
Year2012
SessionJune
TopicDiscrete Random Variables
TypeJoint distribution with independence testing
6 The random variables \(S\) and \(T\) are independent and have joint probability distribution given in the table.
\(S\)
\cline { 2 - 5 }012
\cline { 2 - 5 }1\(a\)0.18\(b\)
20.080.120.20
\cline { 2 - 5 }
\cline { 2 - 5 }
  1. Show that \(a = 0.12\) and find the value of \(b\).
  2. Find \(\mathrm { P } ( T - S = 1 )\).
  3. Find \(\operatorname { Var } ( T - S )\).
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