The prices of stocks S $1,$ S $2,...,$ S $20$ are i$.$i$.$d$.$ uniform random variables on $[10,30].$

a$)$ Suppose that your portfolio consists of $1$ share of each stock. What is the mean and

variance of the total value V of your portfolio?

b$)$ Suppose that your portfolio consists of $20$ shares of stock S $1$ only. What is the

mean and variance of the total value V of your portfolio? Compare with a$),$

which portfolio do you prefer? Why?

c$)$ Suppose that your portfolio consists of $10$ shares of stock S $1$ and $10$ shares of stock

S$21,$ where the price of stock S $21$ is uniform on $[10,30]$ but has perfect negative

correlation $($correlation $=-1)$ with the price of S $1.$ What is the mean and variance of the total value V of your portfolio?