Assume that you can invest $1,000 in a savings account or a fund consisting of different stocks. If you invest in the savings account, you get 1% interest per year. The fund has annual return X with expected value E(X) = 6% and standard deviation o(X) = 20%. This means that, compared to the savings account, the fund has a higher return on average, but also comes with risk. When you invest y dollars in the fund, you will have y(1 + X) dollars after one year. (a) [1 point] If you invest $500 in each the savings account and the fund, what is the expected value of the total investment that you will have after one year? (b) [2 points] Assume that you choose your investment such that the expected value of the return is 4% over one year. How much do you invest of the $1,000 in the fund and the savings account? Hint: set y equal to the terminal value-initial value investment in the fund and write an equation for y using that in general, return = initial value (C) (2 points] Assume that you choose your investment such that the standard deviation of the return is 15% over one year. How much do you invest of the $1,000 in the fund and the savings account? Your investments in the fund and savings account should be positive amounts