If $x is invested in mutual fund I, its worth after one year is distributed
X1 ~ N(1.05x, 0.0002x2)
and if $x is invested in mutual fund II, its worth after one year is distributed
X11 ~ N(1.05x, 0.0003x2)
Suppose that you have $1000 to invest and that you place $y in mutual fund I and $(1000 - y) in mutual fund II.
(a) What is the expected value of the total worth of your investments after one year?
(b) What is the variance of the total worth of your investments after one year?
(c) What value of y minimizes the variance of the total worth of your investments after one year? If you adopt this "conservative" strategy, what is the probability that after one year the total worth of your investments is more than $1060?