OCR MEI Further Statistics A AS 2024 June — Question 1

Exam BoardOCR MEI
ModuleFurther Statistics A AS (Further Statistics A AS)
Year2024
SessionJune
TopicDiscrete Probability Distributions
TypeOne unknown from sum constraint only
1 The probability distribution for a discrete random variable \(X\) is given in the table below.
\(x\)0123
\(\mathrm { P } ( \mathrm { X } = \mathrm { x } )\)\(2 c\)\(3 c\)\(0.5 - c\)\(c\)
  1. Find the value of \(c\).
  2. Find the value of each of the following.
    • \(\mathrm { E } ( X )\)
    • \(\operatorname { Var } ( X )\)
    The random variable \(Y\) is defined by \(Y = 2 X - 3\).
  3. Find the value of each of the following.
    • E(Y)
    • \(\operatorname { Var } ( Y )\)
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