OCR Further Statistics AS 2019 June — Question 1

Exam BoardOCR
ModuleFurther Statistics AS (Further Statistics AS)
Year2019
SessionJune
TopicDiscrete Probability Distributions
TypeExpected profit or cost problem

1 When a spinner is spun, the outcome is equally likely to be 1,2 or 3 . In a competition, the spinner is spun twice and the outcomes are added to give a total score \(T\).
  1. Show that the expectation of \(T\) is 4 .
  2. Find the variance of \(T\). A competitor pays \(\pounds 1.50\) to enter the competition and receives \(\pounds X\), where \(X = 0.3 T\).
    1. Find the expectation of the competitor's profit.
    2. Find the variance of the competitor's profit.