Consider the following information:

State of Economy Probability of State of Economy Rate of Return if State Occurs

Stock A Stock B Stock C

Boom $\mathrm{.}64\mathrm{.}10\mathrm{.}18\mathrm{.}36$

Bust $\mathrm{.}36\mathrm{.}10\mathrm{.}04\mathrm{.}07$

a$.$

What is the expected return on an equally weighted portfolio of these three stocks? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ What is the variance of a portfolio invested $15$ percent each in A and B and $70$ percent in C$?($Do not round intermediate calculations and round your answer to $6$ decimal places, e$.$g$.,\mathrm{.}161616$