4. In a computer game, a ship appears randomly on a rectangular screen. The continuous random variable \(X \mathrm {~cm}\) is the distance of the centre of the ship from the bottom of the screen. The random variable \(X\) is uniformly distributed over the interval \([ 0 , \alpha ]\) where \(\alpha \mathrm { cm }\) is the height of the screen. Given that \(\mathrm { P } ( X > 6 ) = 0.6\)

1. find the value of \(\alpha\)
2. find \(\mathrm { P } ( 4 < X < 10 )\) The continuous random variable \(Y\) cm is the distance of the centre of the ship from the left-hand side of the screen. The random variable \(Y\) is uniformly distributed over the interval [ 0,20 ] where 20 cm is the width of the screen.
3. Find the mean and the standard deviation of \(Y\).
4. Find \(\mathrm { P } ( | Y - 4 | < 2 )\)
5. Given that \(X\) and \(Y\) are independent, find the probability that the centre of the ship appears
   1. in a square of side 4 cm which is at the centre of the screen,
   2. within 5 cm of a side or the top or the bottom of the screen.