2.6.11If $x is invested in mutual fund A, the annual return has anexpectation of $0.1x and a standard deviation of $0.02x. If $x is investedin mutual fund B, the annual return has an expectation of $0.1x and astandard deviation of $0.03x. Suppose that the returns on the two fundsare independent of each other and that I have $1000 to invest.(a) What are the expectation and variance of my annual return if I investall my money in fund A?(b) What are the expectation and variance of my annual return if I investall my money in fund B?(c) What are the expectation and variance of my total annual return if Iinvest half of my money in fund A and half in fund B?(d) Suppose I invest $x in fund A and the rest of my money in fund B. Whatvalue of x minimizes the variance of my total annual return?Explain why your answers illustrate the importance of diversity in aninvestment strategy.

Answered: Image /qna-images/answer/55e6f6e3-75d9-4275-8395-1ca4ccd49e0c.jpg

Answered: in mutual fund B, the annual return has…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose that the City of Chicago is interested in potential revenues if they introduce a tolling station near O'Hare. Further suppose that the average time between cars is only 2.5 seconds; what is the likelihood that the next car comes in more than 2.2 seconds? Round your answer to two decimal places.
Suppose that you just bought a painting for $1million. You plan to sell it exactly one year fromnow. You don’t know what the exact price will bewhen you sell. Nevertheless, you believe thatthere’s a 65% chance that you can sell it for$1.2million, and a 35% chance that you can sell itfor only $900,000. What is your expected gain orloss for this investment?
The accompanying data represent the annual rates of return of two companies' stock for the past 12 years. Complete parts (a) through (k). O A. OB. 0.50- 0.50- 0.00- 0.00- -0.50- -0.50- -0.3 RR of Company 2 0.0 0.3 -0.3 0.0 0.3 RR of Company 1 OC. 0.30- 0.50- 0.00- 0.00- -0.30- -0.50- o.0 0'5 0.0 0.3 -0.5 RR of Company 2 0.5 -0.3 RR of Company 1 (b) Determine the correlation coefficient between rate of return of Company 1 and Company 2. The correlation coefficient is 0.966. (Round to three decimal places as needed.) (c) Based on the scatter diagram and correlation coefficient, is there a linear relation between rate of return of Company 1 and Company 2? Yes No (d) Find the least-squares regression line treating the rate of return of Company 1 as the explanatory variable. y=x+O (Round to four decimal places as needed.) RR of Company 1 RR of Company 1 RR of Company 2 RR of Company 2
.A new, miracle diabetes drug that diminishes major symptoms of diabetes has been approved by the FDA. Health care professionals and researchers believe that the new drug will prolong lifespan of diabetes patients. If the population is in steady state and the incidence is constant, what will the effect of this new drug be on the prevalence of diabetes in the population? Explain.
4. Along with interest rates, life expectancy is a component in pricing financial annuities. Suppose that you know that last year average life expectancy was 77 years for your annuity holders. Now you want to know if your clients this year have a longer life expectancy, on average, so you randomly sample n=20 of your recently deceased annuity holders to see actual age at death. Using a 5% level of significance, test whether or not the new data shows evidence of your annuity holders now live longer than 77 years, on average. The data below are the sample data (in years of life): (78,75,83,81,81,77,78,79,79,81,76,79,77,76,79,81,73,74,78,79) a) Does this sample indicate that life expectancy has increased? Test an appropriate hypothesis and state your conclusion (use a 5% level of significance). Be sure to check the necessary assumptions and conditions before conducting your test. b) Construct A 90% confidence interval for the true average age of death for the population of your annuity…
The selling prices of mutual funds change daily. In order to study these changes, a sample of mutual funds was examined and the daily changes in price are listed below. (Round answers to 3 decimal places) 0.32, -0.17, 0.26, -0.03, -0.01, 0.18, 0.33, 0.28, 0.02, -0.29, -0.08, 0.12, 0.07, 0.03, 0.28 a) Using a calculator find Q1, Q3, median and IQR b) Determine the lower and upper fences. (Show work) c) Identify the outliers (if any) in this set
Suppose that the City of Chicago is interested in potential revenues if they introduce a tolling station near O'Hare. Further suppose that the average time between cars is only 1.8 seconds; what is the likelihood that the next car comes within 3.5 seconds? Round your answer to two decimal places.
When it is sunny, Joe's ice cream truck generates a profit of $547 per day, when it is not sunny, the profit is $250 per day, and when the truck is not out there selling ice cream, Joe loses $120 per day. Suppose 8% of a year Joe's truck is on vacation, and 86% of a year the truck is selling ice cream on sunny days, what is the expected daily profit the truck generates over a year? Enter answer as a decimal rounded to TWO digits after the decimal point.
Below are percentages for annual sales growth and net sales attributed to loyalty card usage at 74 Noodles & Company restaurants. Annual Sales Growth (px;) and Loyalty Card Usage (px; of Net Sales)(n = 74 restaurants) Store Growth% Loyalty% Store Growth% Loyalty% 1 -7.8 0.7 38 7.3 1.5 2 -6.9 2.5 39 7.4 1.7 3 -5.1 1.6 40 7.7 2.3 4 -4.7 1.4 41 8.0 2.0 5 -3.8 2.5 42 8.0 1.6 6 -1.7 1.5 43 8.3 1.9 7 -1.7 2.6 44 8.4 2.0 8 -1.6 2.4 45 8.6 2.2 9 -1.1 2.2 46 8.6 1.6 10 -1.0 1.9 47 8.7 0.9 11 0.4 1.2 48 8.9 1.7 12 0.6 0.5 49 9.4 1.6 13 0.6 2.1 50 9.5 1.3 14 1.0 1.3 51 9.5 2.1 15 1.3 2.0 52 10.5…
A certain brokerage house wants to estimate the mean daily return on a certain stock. A random sample of 12 days yields the following return percentages.−1.81, 1.54, 1.52, −2.58, −2.3, 0.97, 0.93, −1.06, 1.04, 0.2, −0.63, −2.75 Send data to calculator If we assume that the returns are normally distributed, find a 90% confidence interval for the mean daily return on this stock. Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.) Lower limit: ? Upper limit: ?
A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 34,000 miles and a standard deviation of 2200 miles. He wants to give a guarantee for free replacement of tires that don't wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires? Click to view page 1 of the table. Click to view page 2 of the table. ****... Tires that wear out by miles will be replaced free of charge. (Round to the nearest mile as needed.)

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