Edexcel S1 2014 June — Question 1

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2014
SessionJune
TopicDiscrete Probability Distributions
TypeOne unknown from sum constraint only

  1. The discrete random variable \(X\) has probability distribution
\(x\)- 4- 2135
\(\mathrm { P } ( X = x )\)0.4\(p\)0.050.15\(p\)
  1. Show that \(p = 0.2\) Find
  2. \(\mathrm { E } ( X )\)
  3. \(\mathrm { F } ( 0 )\)
  4. \(\mathrm { P } ( 3 X + 2 > 5 )\) Given that \(\operatorname { Var } ( X ) = 13.35\)
  5. find the possible values of \(a\) such that \(\operatorname { Var } ( a X + 3 ) = 53.4\)