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In: Statistics and Probability

You are considering two investments. Let X represent the proportional rate of return on the first...

You are considering two investments. Let X represent the proportional rate of return on the first investment, and let Y represent the proportional rate of return on the second investment. These are annual rates of return.

X is approximately normally distributed with mean 0.35 and standard deviation 0.3. Y is approximately normally distributed with mean 0.40 and standard deviation 0.5.

These six questions are about the rates of return, X and Y.

1. What is the probability of a negative rate of return on the first investment?  3 decimals.

2. What is the probability of a negative rate of return on the second investment?  3 decimals.

3. If the rates of return on these investments are independent, what is the probability that the rates of return on both investments will be negative?  3 decimals.

4. What is the expected amount by which Y exceeds X? HINT: The amount by which the rate of return on the second investment is higher than the rate of return on the first investment is Y - X.   2 decimals.

5. If the rates of return on these investments are independent, what is the probability that the second investment will have a higher rate of return than the first? HINT: Restate the question in terms of the rate of return on the second investment minus the rate of return on the first investment.  3 decimals.

6. If instead X and Y have a correlation of – 0.5 (a negative correlation), what is the probability that the second investment will have a higher rate of return than the first? HINT: Be careful! You’re given the correlation, not the covariance!  3 decimals.

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orchestra answered 1 year ago
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