SPS SPS FM Statistics 2022 February — Question 1

Exam BoardSPS
ModuleSPS FM Statistics (SPS FM Statistics)
Year2022
SessionFebruary
TopicDiscrete Probability Distributions
TypeCalculate E(X) from given distribution

  1. The random variable \(X\) represents the clutch size (the number of eggs laid) by female birds of a particular species. The probability distribution of \(X\) is given in the table.
\(r\)234567
\(\mathrm { P } ( X = r )\)0.030.070.270.490.130.01
  1. Find each of the following.
    • \(\mathrm { E } ( X )\)
    • \(\operatorname { Var } ( X )\)
    On average \(65 \%\) of eggs laid result in a young bird successfully leaving the nest.
    1. Find the mean number of young birds that successfully leave the nest.
    2. Find the standard deviation of the number of young birds that successfully leave the nest.
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