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.
| \(r\) | 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.