$3.$ Suppose you have two assets in your portfolio; A and B$.$ Suppose the weight of A is $0\mathrm{.}35$ and the weight of B is $0\mathrm{.}65.$ Also, suppose that the standard deviation of A is $10\%$ and the standard deviation of B is $12\%.$ Compute the variance of the portfolio under the following cases:

a$.$ The correlation coefficient between A and B is $0\mathrm{.}5$

b$.$ The correlation coefficient between A and B is $0\mathrm{.}8$

c$.$ Why the risk of a portfolio is not the weighted average of individual risks of each

asset in the portfolio?