OCR S1 2014 June — Question 2

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2014
SessionJune
TopicDiscrete Probability Distributions
TypeCalculate Var(X) from table
2
  1. The probability distribution of a random variable \(W\) is shown in the table.
    \(w\)024
    \(\mathrm { P } ( W = w )\)0.30.40.3
    Calculate \(\operatorname { Var } ( W )\).
  2. The random variable \(X\) has probability distribution given by $$\mathrm { P } ( X = x ) = k ( x + 1 ) \quad \text { for } x = 1,2,3,4 .$$
    1. Show that \(k = \frac { 1 } { 14 }\).
    2. Calculate \(\mathrm { E } ( X )\).
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