Edexcel S1 2015 January — Question 1

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2015
SessionJanuary
TopicCumulative distribution functions
TypeDiscrete CDF to PMF
  1. The discrete random variable \(X\) has probability function \(\mathrm { p } ( x )\) and cumulative distribution function \(\mathrm { F } ( x )\) given in the table below.
\(x\)12345
\(\mathrm { p } ( x )\)0.10\(a\)0.28\(c\)0.24
\(\mathrm {~F} ( x )\)0.100.26\(b\)0.76\(d\)
  1. Write down the value of \(d\)
  2. Find the values of \(a\), \(b\) and \(c\)
  3. Write down the value of \(\mathrm { P } ( X > 4 )\) Two independent observations, \(X _ { 1 }\) and \(X _ { 2 }\), are taken from the distribution of \(X\).
  4. Find the probability that \(X _ { 1 }\) and \(X _ { 2 }\) are both odd. Given that \(X _ { 1 }\) and \(X _ { 2 }\) are both odd,
  5. find the probability that the sum of \(X _ { 1 }\) and \(X _ { 2 }\) is 6 Give your answer to 3 significant figures.
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