OCR S1 2015 June — Question 9

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2015
SessionJune
TopicDiscrete Probability Distributions
TypeTwo unknowns from sum and expectation

9 The random variable \(X\) has probability distribution given by $$\mathrm { P } ( X = x ) = a + b x \quad \text { for } x = 1,2 \text { and } 3 ,$$ where \(a\) and \(b\) are constants.
  1. Show that \(3 a + 6 b = 1\).
  2. Given that \(\mathrm { E } ( X ) = \frac { 5 } { 3 }\), find \(a\) and \(b\).