OCR S1 2006 June — Question 5

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2006
SessionJune
TopicDiscrete Probability Distributions
TypeTwo unknowns from sum and expectation
5 The probability distribution of a discrete random variable, \(X\), is given in the table.
\(x\)0123
\(\mathrm { P } ( X = x )\)\(\frac { 1 } { 3 }\)\(\frac { 1 } { 4 }\)\(p\)\(q\)
It is given that the expectation, \(\mathrm { E } ( X )\), is \(1 \frac { 1 } { 4 }\).
  1. Calculate the values of \(p\) and \(q\).
  2. Calculate the standard deviation of \(X\).
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