Edexcel S1 2010 January — Question 5

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2010
SessionJanuary
TopicDiscrete Probability Distributions
TypeSimple algebraic expression for P(X=x)
5. The probability function of a discrete random variable \(X\) is given by $$\mathrm { p } ( x ) = k x ^ { 2 } \quad x = 1,2,3$$ where \(k\) is a positive constant.
  1. Show that \(k = \frac { 1 } { 14 }\) Find
  2. \(\mathrm { P } ( X \geqslant 2 )\)
  3. \(\mathrm { E } ( X )\)
  4. \(\operatorname { Var } ( 1 - X )\)
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