Take fourth moments when an area is proportional to the square

S has distribution

s	$P(S=s)$
1	0.5
5	0.3
10	0.1
20	0.1

A circle has radius $R=2S$.

(i) Find $P(S(11-S)\le10)$.3 marks

(ii) Find $E(S)$ and $\operatorname{Var}(S)$.3 marks

(iii) Hence find the mean and variance of the circle’s area A.5 marks