Edexcel S1 2004 November — Question 4

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2004
SessionNovember
TopicDiscrete Probability Distributions
TypeOne unknown from sum constraint only

4. The discrete random variable \(X\) has probability function $$\mathrm { P } ( X = x ) = \begin{array} { l l } 0.2 , & x = - 3 , - 2
\alpha , & x = - 1,0
0.1 , & x = 1,2 . \end{array}$$ Find
  1. \(\alpha\),
  2. \(\mathrm { P } ( - 1 \leq X < 2 )\),
  3. \(\mathrm { F } ( 0.6 )\),
  4. the value of \(a\) such that \(\mathrm { E } ( a X + 3 ) = 1.2\),
  5. \(\operatorname { Var } ( X )\),
  6. \(\operatorname { Var } ( 3 X - 2 )\).