Consider the following information:

Rate of Return if State Occurs

State of Economy Probability of

State of Economy Stock A Stock B Stock C

Boom $0\mathrm{.}640\mathrm{.}130\mathrm{.}130\mathrm{.}07$

Bust $0\mathrm{.}360\mathrm{.}070\mathrm{.}170\mathrm{.}15$

a$.$ What is the expected return on an equally weighted portfolio of these three stocks?

b$.$ What is the variance of a portfolio invested $20$ percent each in A and B and $60$ percent in C$?$