3 A particular type of bird lays 1,2,3 or 4 eggs in a nest each year. The probability of \(x\) eggs is equal to \(k x\), where \(k\) is a constant.
- Draw up a probability distribution table, in terms of \(k\), for the number of eggs laid in a year and find the value of \(k\).
- Find the mean and variance of the number of eggs laid in a year by this type of bird.