a$)$ The table below shows the performance of two shares A and B under four different economic conditions and their associated probabilities of occurrence:

Economic Condition Rate of return $\%$ Rate of return $\%$ Probabilities Probabilities

A B A B

Growth $18\mathrm{.}5016\mathrm{.}500\mathrm{.}250\mathrm{.}45$

Expansion $12\mathrm{.}7514\mathrm{.}000\mathrm{.}250\mathrm{.}20$

Stagnation $1\mathrm{.}251\mathrm{.}800\mathrm{.}250\mathrm{.}20$

Recession $-6\mathrm{.}00-4\mathrm{.}500\mathrm{.}250\mathrm{.}15$

Calculate:

i$)$ The expected rate of return for shares A and B$.(6$mks$)$

ii$)$ The standard deviation of the returns for shares A and B$.(8$mks$)$

iii$)$ The coefficient of variation of returns for shares A and B$.(4$mks$)$

iv$)$ Advise an investor on the preferred share. $(2$mks$)$