Edexcel S1 2019 January — Question 2

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2019
SessionJanuary
TopicDiscrete Probability Distributions
TypeTwo unknowns from sum and expectation
2. The discrete random variable \(X\) has the following probability distribution.
\(x\)- 2- 1013
\(\mathrm { P } ( X = x )\)0.15\(a\)\(b\)\(a\)0.4
  1. Find \(\mathrm { E } ( X )\). Given that \(\mathrm { E } \left( X ^ { 2 } \right) = 4.54\)
  2. find the value of \(a\) and the value of \(b\). The random variable \(Y = 3 - 2 X\)
  3. Find \(\operatorname { Var } ( Y )\).
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