Edexcel S2 2011 January — Question 3

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Year2011
SessionJanuary
TopicContinuous Uniform Random Variables
TypeMultiple observations or trials

3. The continuous random variable \(X\) is uniformly distributed over the interval \([ - 1,3 ]\). Find
  1. \(\mathrm { E } ( X )\)
  2. \(\operatorname { Var } ( X )\)
  3. \(\mathrm { E } \left( X ^ { 2 } \right)\)
  4. \(\mathrm { P } ( X < 1.4 )\) A total of 40 observations of \(X\) are made.
  5. Find the probability that at least 10 of these observations are negative.