OCR MEI S1 — Question 5

Exam BoardOCR MEI
ModuleS1 (Statistics 1)
TopicDiscrete Probability Distributions
TypeSimple algebraic expression for P(X=x)
5 The probability distribution of the random variable \(X\) is given by the formula $$\mathrm { P } ( X = r ) = k r ( 5 - r ) \text { for } r = 1,2,3,4$$
  1. Show that \(k = 0.05\).
  2. Find \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).
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