CAIE S1 2019 March — Question 4

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2019
SessionMarch
TopicDiscrete Probability Distributions
TypeSimple algebraic expression for P(X=x)

4 The random variable \(X\) takes the values \(- 1,1,2,3\) only. The probability that \(X\) takes the value \(x\) is \(k x ^ { 2 }\), where \(k\) is a constant.
  1. Draw up the probability distribution table for \(X\), in terms of \(k\), and find the value of \(k\).
  2. Find \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).