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I am working through review problems and was stuck on this question, could you please guide...

I am working through review problems and was stuck on this question, could you please guide me on how to approach this type of problem? Thank you!

You are investing your money in two hedge funds and want to split your cash among two funds, Fund A and Fund B. If you invest $x dollars in Fund A, its worth after one year is distributed as a Normal (µA = 1.05x, σA2 = .02x2 ). If instead you invest $x dollars in Fund B, its worth after one year is distributed as a Normal (µB = 1.05x, σB2 = .03x2 ). Suppose you invest $p in Fund A and $(100 - p) in Fund B where p ∈ [0, 100] and both funds are independent.

(a) What is the expected value of the total worth of your investment after one year?

(b) What is the variance of the total worth of your investment after one year?

(c) What is the value of p which minimizes the variance of the total worth of your investment after one year? (d) If you adopt the value of p you determined in part (c), what is the probability that after one year the total worth of your investment is more than $120?

Math   Statistics-And-Probability   
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