SPS SPS FM Statistics 2022 February — Question 3

Exam BoardSPS
ModuleSPS FM Statistics (SPS FM Statistics)
Year2022
SessionFebruary
TopicGeometric Distribution
TypeFirst success on specific trial

3. A football player is practising taking penalties. On each attempt the player has a \(70 \%\) chance of scoring a goal. The random variable \(X\) represents the number of attempts that it takes for the player to score a goal.
  1. Determine \(\mathrm { P } ( X = 4 )\).
  2. Find each of the following.
    • \(\mathrm { E } ( X )\)
    • \(\operatorname { Var } ( X )\)
    • Determine the probability that the player needs exactly 4 attempts to score 2 goals.
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