- The random variable \(W\) has a discrete uniform distribution where
$$\mathrm { P } ( W = w ) = \frac { 1 } { 5 } \quad \text { for } w = 1,2,3,4,5$$
- Find \(\mathrm { P } ( 2 \leqslant W < 3.5 )\)
The discrete random variable \(X = 5 - 2 W\)
- Find \(\mathrm { E } ( X )\)
- Find \(\mathrm { P } ( X < W )\)
The discrete random variable \(\mathrm { Y } = \frac { 1 } { W }\)
- Find
- the probability distribution of \(Y\)
- \(\operatorname { Var } ( Y )\), showing your working.
- Find \(\operatorname { Var } ( 2 - 3 Y )\)