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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 2.6 - Problem 23e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 2.6 - Problem 23e

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# An investor has $100 to invest, and two investments ISBN: 9780073401331 38 ## Solution for problem 23E Chapter 2.6 Statistics for Engineers and Scientists | 4th Edition • Textbook Solutions • 2901 Step-by-step solutions solved by professors and subject experts • Get 24/7 help from StudySoup virtual teaching assistants Statistics for Engineers and Scientists | 4th Edition 4 5 1 294 Reviews 27 2 Problem 23E Problem 23E An investor has$100 to invest, and two investments between which to divide it. If she invests the entire amount in the first investment, her return will be X, while if she invests the entire amount in the second investment, her return will be Y. Both X and Y have mean $6 and standard deviation (risk)$3. The correlation between X and Y is 0.3.

a. Express the return in terms of X and Y if she invests $30 in the first investment and$70 in the second.

b. Find the mean return and the risk if she invests $30 in the first investment and$70 in the second.

c. Find the mean return and the risk, in terms of K, if she invests $K in the first investment and$(100- K) in the second.

d. Find the value of K that minimizes the risk in part (c).

e. Prove that the value of K that minimizes the risk in part (c) is the same for any correlation ρX,Y with ρX,Y ≠ 1.

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