Question 1

Investment advisors recommend risk reduction through international diversification. Laura, a portfolio manager, is considering taking advantage of the potential for growth in foreign economies, particularly in Europe or Asia. She has studied these markets and believes that both markets will be influenced by the U.S. economy. The table below shows the expected returnof each of these investments under various economic conditions and the probability that each of those economic conditions will occur.

Probability	U.S. Economic Condition	Returns in Europe (%)	Returns in Asia (%)
0.05	Extreme recession	-2%	-100%
0.10	Recession	-7%	-30%
0.17	Stagnation	3%	-10%
0.22	Slow growth	8%	10%
0.38	Moderate growth	10%	15%
0.08	High growth	12%	35%

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1. Find the expected annual return for Europe.
2. Find the expected annual return for Asia.
3. Find the standard deviation of the annual return for Europe.
4. Find the standard deviation of the annual return for Asia.
5. Find the covariance between the annual return of Europe and Asia.
6. Find the correlation between the annual return of Europe and Asia.

Laura has 10 million dollars to invest, and she decides to form a portfolio by investing 6.8 million dollars in Europe and the rest in Asia.

1. What is the expected return from such a portfolio?
2. Compute the standard deviation of the above portfolio.
3. Using the standard deviation as a measure of financial risk (volatility), how does the risk of the above portfolio compare with the risk of the individual components: Europeand Asia?

Question 2

According to IDC, 63% of smartphone shipments in the world were Apple in the fourth quarter of 2022. Answers the following questions based on a random sample of 14 smartphone shipments to customers.

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1. What is the probability that exactly 4 people from this sample have an Apple smartphone?
2. What is the probability that all 14 people from this sample have an Apple smartphone?
3. What is the probability that 12 or fewer people from this sample have an Apple smartphone?
4. What are the mean and standard deviation for this distribution?

Question 3

John is an employee at a customer service call center for a large retail company. Historically, John has averaged 43 complaint calls per day. Assume the number of calls that John completes per day follows the Poisson distribution.

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1. What is the probability that John will complete 47 complaint calls tomorrow?
2. What is the probability that John will complete fewer than 34 complaint calls tomorrow?
3. What is the probability that John will complete more than 40 complaint calls tomorrow?
4. What is the mean and standard deviation for this distribution?