4 The number, \(X\), of children per family in a certain city is modelled by the probability distribution \(\mathrm { P } ( X = r ) = k ( 6 - r ) ( 1 + r )\) for \(r = 0,1,2,3,4\).
- Copy and complete the following table and hence show that the value of \(k\) is \(\frac { 1 } { 50 }\).
| \(r\) | 0 | 1 | 2 | 3 | 4 |
| \(\mathrm { P } ( X = r )\) | \(6 k\) | \(10 k\) | | | |
- Calculate \(\mathrm { E } ( X )\).
- Hence write down the probability that a randomly selected family in this city has more than the mean number of children.