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.
\(r\)
2
3
4
5
6
7
\(\mathrm { P } ( X = r )\)
0.03
0.07
0.27
0.49
0.13
0.01
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.
Find the mean number of young birds that successfully leave the nest.
Find the standard deviation of the number of young birds that successfully leave the nest. [0pt]
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