Edexcel S1 2006 January — Question 2

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2006
SessionJanuary
TopicDiscrete Probability Distributions
TypeTwo unknowns from sum and expectation
2. The random variable \(X\) has probability distribution
\(x\)12345
\(\mathrm { P } ( X = x )\)0.10\(p\)0.20\(q\)0.30
  1. Given that \(\mathrm { E } ( X ) = 3.5\), write down two equations involving \(p\) and \(q\). Find
  2. the value of \(p\) and the value of \(q\),
  3. \(\operatorname { Var } ( X )\),
  4. \(\operatorname { Var } ( 3 - 2 X )\).
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