Edexcel S2 2023 June — Question 6

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Year2023
SessionJune
TopicContinuous Uniform Random Variables
TypeFind parameters from given statistics

  1. Akia selects at random a value from the continuous random variable \(W\), which is uniformly distributed over the interval \([ a , b ]\)
The probability that Akia selects a value greater than 17 is \(\frac { 1 } { 5 }\) The probability that Akia selects a value less than \(k\) is \(\frac { 53 } { 60 }\)
  1. Find the probability that Akia selects a value between 17 and \(k\) It is known that \(\operatorname { Var } ( W ) = 75\)
    1. Find the value of \(a\) and the value of \(b\)
    2. Find the value of \(k\)
  2. Find \(\mathrm { P } ( - 5 < W < 5 )\)
  3. Find \(\mathrm { E } \left( W ^ { 2 } \right)\)