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

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