OCR S1 2008 January — Question 6

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2008
SessionJanuary
TopicDiscrete Probability Distributions
TypeSum or product of two independent values
6 The probability distribution for a random variable \(Y\) is shown in the table.
\(y\)123
\(\mathrm { P } ( Y = y )\)0.20.30.5
  1. Calculate \(\mathrm { E } ( Y )\) and \(\operatorname { Var } ( Y )\). Another random variable, \(Z\), is independent of \(Y\). The probability distribution for \(Z\) is shown in the table.
    \(z\)123
    \(\mathrm { P } ( Z = z )\)0.10.250.65
    One value of \(Y\) and one value of \(Z\) are chosen at random. Find the probability that
  2. \(Y + Z = 3\),
  3. \(Y \times Z\) is even.
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