CAIE S1 2023 November — Question 1

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2023
SessionNovember
TopicDiscrete Probability Distributions
TypeTwo unknowns from sum and expectation

1 A competitor in a throwing event has three attempts to throw a ball as far as possible. The random variable \(X\) denotes the number of throws that exceed 30 metres. The probability distribution table for \(X\) is shown below.
\(x\)0123
\(\mathrm { P } ( X = x )\)0.4\(p\)\(r\)0.15
  1. Given that \(\mathrm { E } ( X ) = 1.1\), find the value of \(p\) and the value of \(r\).
  2. Find the numerical value of \(\operatorname { Var } ( X )\).