Edexcel Paper 3 2021 October — Question 6

Exam BoardEdexcel
ModulePaper 3 (Paper 3)
Year2021
SessionOctober
TopicDiscrete Probability Distributions
TypeOne unknown from sum constraint only

  1. The discrete random variable \(X\) has the following probability distribution
\(x\)\(a\)\(b\)\(c\)
\(\mathrm { P } ( X = x )\)\(\log _ { 36 } a\)\(\log _ { 36 } b\)\(\log _ { 36 } c\)
where
  • \(\quad a , b\) and \(c\) are distinct integers \(( a < b < c )\)
  • all the probabilities are greater than zero
    1. Find
      1. the value of a
      2. the value of \(b\)
      3. the value of \(c\)
Show your working clearly. The independent random variables \(X _ { 1 }\) and \(X _ { 2 }\) each have the same distribution as \(X\)
  • Find \(\mathrm { P } \left( X _ { 1 } = X _ { 2 } \right)\) \section*{Question 6 continued.} \section*{Question 6 continued.}