OCR S1 2013 January — Question 5

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2013
SessionJanuary
TopicBinomial Distribution
TypeIndependent binomial samples with compound probability

5 A random variable \(X\) has the distribution \(\mathrm { B } \left( 5 , \frac { 1 } { 4 } \right)\).
  1. Find
    (a) \(\mathrm { E } ( X )\),
    (b) \(\mathrm { P } ( X = 2 )\).
  2. Two values of \(X\) are chosen at random. Find the probability that their sum is less than 2 .
  3. 10 values of \(X\) are chosen at random. Use an appropriate formula to find the probability that exactly 3 of these values are 2 s .