OCR MEI Further Statistics Minor 2019 June — Question 6

Exam BoardOCR MEI
ModuleFurther Statistics Minor (Further Statistics Minor)
Year2019
SessionJune
TopicBivariate data
TypeCalculate r from summary statistics

6 The discrete random variable \(X\) has a uniform distribution over \(\{ n , n + 1 , \ldots , 2 n \}\).
  1. Given that \(n\) is odd, find \(\mathrm { P } \left( X < \frac { 3 } { 2 } n \right)\).
  2. Given instead that \(n\) is even, find \(\mathrm { P } \left( X < \frac { 3 } { 2 } n \right)\), giving your answer as a single algebraic fraction.
  3. The sum of 6 independent values of \(X\) is denoted by \(Y\). Find \(\operatorname { Var } ( Y )\).