Edexcel S1 2012 January — Question 3

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2012
SessionJanuary
TopicDiscrete Probability Distributions
TypeProbabilities in table form with k

3. The discrete random variable \(X\) can take only the values \(2,3,4\) or 6 . For these values the probability distribution function is given by
\(x\)2346
\(\mathrm { P } ( X = x )\)\(\frac { 5 } { 21 }\)\(\frac { 2 k } { 21 }\)\(\frac { 7 } { 21 }\)\(\frac { k } { 21 }\)
where \(k\) is a positive integer.
  1. Show that \(k = 3\) Find
  2. \(\mathrm { F } ( 3 )\)
  3. \(\mathrm { E } ( X )\)
  4. \(\mathrm { E } \left( X ^ { 2 } \right)\)
  5. \(\operatorname { Var } ( 7 X - 5 )\)