You have been provided with the following information for two investments A and B$.$

State of the economy Probability Returns of A $(\%)$ Returns of B $(\%)$

Boom $0\mathrm{.}4209$

Normal $0\mathrm{.}31512$

Recession $0\mathrm{.}31018$

a$)$ Calculate the expected return and standard deviation of projects A and B$.$

b$)$ If projects A and B are combined in the ratio $6$:$4,$ what will be the expected return and standard

deviation of the portfolio?