Consider the following scenario analysis:

Scenario Rate Of Return

Recession: Probability: $0\mathrm{.}3$ Stocks: $6\%$ Bonds: $14\%$

Normal economy: Proability: $0\mathrm{.}6$ Stocks: $15$ Bonds: $11$

Boom: Probability: $0\mathrm{.}1$ Stocks: $24$ Bonds: $5$

Assume a portfolio with weights of $0\mathrm{.}60$ in stocks and $0\mathrm{.}40$ in bonds.

a$)$ What is the rate of return on the portfolio in each scenario?

b$)$ What are the expected rate of return and standard deviation of the portfolio?