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 $0\mathrm{.}780\mathrm{.}130\mathrm{.}170\mathrm{.}21$

Bust $0\mathrm{.}220\mathrm{.}170\mathrm{.}090\mathrm{.}01$

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$?$