CAIE S1 2023 June — Question 1

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2023
SessionJune
TopicDiscrete Probability Distributions
TypeSimple algebraic expression for P(X=x)

1 The random variable \(X\) takes the values \(- 2,2\) and 3. It is given that $$\mathrm { P } ( X = x ) = k \left( x ^ { 2 } - 1 \right)$$ where \(k\) is a constant.
  1. Draw up the probability distribution table for \(X\), giving the probabilities as numerical fractions.
  2. Find \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).