Edexcel S1 2023 October — Question 4

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2023
SessionOctober
TopicDiscrete Probability Distributions
TypeCalculate Var(X) from table
  1. The discrete random variable \(X\) has the following probability distribution.
\(x\)1234
\(\mathrm { P } ( X = x )\)\(\frac { 1 } { 10 }\)\(\frac { 1 } { 5 }\)\(\frac { 3 } { 10 }\)\(\frac { 2 } { 5 }\)
  1. Show that \(\mathrm { E } \left( \frac { 1 } { X } \right) = \frac { 2 } { 5 }\)
  2. Find \(\operatorname { Var } \left( \frac { 1 } { X } \right)\) The random variable \(Y = \frac { 30 } { X }\)
  3. Find
    1. \(\mathrm { E } ( Y )\)
    2. \(\operatorname { Var } ( Y )\)
  4. Find \(\mathrm { P } ( X < 3 \mid Y < 20 )\)
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