SPS SPS FM Statistics 2024 September — Question 3

Exam BoardSPS
ModuleSPS FM Statistics (SPS FM Statistics)
Year2024
SessionSeptember
TopicGeometric Distribution
TypeVariance of geometric distribution
3. The random variable \(D\) has the distribution \(\operatorname { Geo } ( p )\). It is given that \(\operatorname { Var } ( D ) = \frac { 40 } { 9 }\).
Determine
  1. \(\operatorname { Var } ( 3 D + 5 )\),
  2. \(\mathrm { E } ( 3 D + 5 )\),
  3. \(\mathrm { P } ( D > \mathrm { E } ( D ) )\).
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