Edexcel S1 2024 January — Question 7

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2024
SessionJanuary
TopicCumulative distribution functions
TypeDiscrete CDF table with constants
  1. The cumulative distribution of a discrete random variable \(X\) is given by
\(x\)1234
\(\mathrm {~F} ( x )\)\(\frac { 1 } { 13 }\)\(\frac { 2 k - 1 } { 26 }\)\(\frac { 3 ( k + 1 ) } { 26 }\)\(\frac { k + 4 } { 8 }\)
where \(k\) is a positive constant.
  1. Show that \(k = 4\)
  2. Find the probability distribution of the discrete random variable \(X\)
  3. Using your answer to part (b), write down the mode of \(X\)
  4. Calculate \(\operatorname { Var } ( 13 X - 6 )\)
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