OCR MEI Further Statistics Major 2021 November — Question 9

Exam BoardOCR MEI
ModuleFurther Statistics Major (Further Statistics Major)
Year2021
SessionNovember
TopicSequences and series, recurrence and convergence

9 The discrete random variable \(X\) has a uniform distribution over the set of all integers between \(- n\) and \(n\) inclusive, where \(n\) is a positive integer.
  1. Given that \(n\) is odd, determine \(\mathrm { P } \left( \mathrm { X } > \frac { 1 } { 2 } \mathrm { n } \right)\), giving your answer as a single fraction in terms of \(n\).
  2. Determine the variance of the sum of 10 independent values of \(X\), giving your answer in the form \(\mathrm { an } ^ { 2 } + \mathrm { bn }\), where \(a\) and \(b\) are constants.