CAIE S1 2021 March — Question 4

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2021
SessionMarch
TopicDiscrete Probability Distributions
TypeSimple algebraic expression for P(X=x)
4 The random variable \(X\) takes the values \(1,2,3,4\) only. The probability that \(X\) takes the value \(x\) is \(k x ( 5 - x )\), where \(k\) is a constant.
  1. Draw up the probability distribution table for \(X\), in terms of \(k\).
  2. Show that \(\operatorname { Var } ( X ) = 1.05\).
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