Edexcel S1 2010 June — Question 3

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2010
SessionJune
TopicDiscrete Probability Distributions
TypeOne unknown from sum constraint only
3. The discrete random variable \(X\) has probability distribution given by
\(x\)- 10123
\(\mathrm { P } ( X = x )\)\(\frac { 1 } { 5 }\)\(a\)\(\frac { 1 } { 10 }\)\(a\)\(\frac { 1 } { 5 }\)
where \(a\) is a constant.
  1. Find the value of \(a\).
  2. Write down \(\mathrm { E } ( X )\).
  3. Find \(\operatorname { Var } ( X )\). The random variable \(Y = 6 - 2 X\)
  4. Find \(\operatorname { Var } ( Y )\).
  5. Calculate \(\mathrm { P } ( X \geqslant Y )\).
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