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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1Consider the information below relating to the monthly rates of return for two companies X and Y over a period of 4 months: Y 2 xRate of return yRate of Return Date Month 1 -4.76 -4.75 Month 2 5.34 7.65 Month 3 12.09 6.98 Month 4 -2.98 9.65 Calculate the covariance per month between the two companies. Show all your working.
- If X is a random variable with expectation µ and variance cµ2 , where c is a constant. Find a variance stabilizing transformation of X.Suppose in a Country Waffleland, there are two socio-economic classes. The workingclass accounts for 90% of the population. Each person in the working class has awealth of w, where w > 0. The rest of the society consists of people with inheritedwealth. Each person in this class has a wealth of 9w. What is the Gini coefficientof the wealth distribution in this country?Assume that security returns are generated by the single-index model, Ri = αi + βiRM + ei where Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 3%. Suppose also that there are three securities A, B, and C, characterized by the following data: Security βi E(Ri) σ(ei) A 1.4 14 % 23 % B 1.6 16 14 C 1.8 18 17 a. If σM = 22%, calculate the variance of returns of securities A, B, and C. b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number.)
- Suppose that index model for Stocks A and B is estimated from excess returns with the following results : Ra 0.04 +0.6Rm+ea , Rb = - 0.04 + 1.3Rm + eb Risk on the market is 30% , R-squared of A is 30%R - squared of B is 40% , security A residual variance isHuman blood types are classified by three gene forms A, B, and O. Blood types AA, BB, and OO are homozygous, and blood types AB, AO, and BO are heterozygous. If p, q, and r represent the proportions of the three gene forms to the popula-tion, respectively, then the Hardy-Weinberg Law asserts that the proportion Q of heterozygous persons in any specific population is modeled by Q(p, q, r) = 2(pq + pr + qr), subject to p + q + r = 1. Find the maximum value of Q.d. What is the detection limit for the method?
- The populations, P, of six towns at time t in years are given by(i) P=2,090(1.08)t(ii) P=560(1.12)t(iii) P=2,700(0.9)t(iv) P=1200(1.18)t(v) P=800(0.78)t(vi) P=2000(0.99)t (a) Which towns are growing in size? Which are shrinking? Select all that apply.Growing towns: (i) (ii) (iii) (iv) (v) (vi) Shrinking towns: (i) (ii) (iii) (iv) (v) (vi) (b) Which town is growing the fastest? What is the annual percent growth rate for that town?Town (Click for List)(i)(ii)(iii)(iv)(v)(vi) is growing the fastest. It is growing at a rate of % per year. (c) Which town is shrinking the fastest? What is the annual percent decay rate for that town? Town (Click for List)(i)(ii)(iii)(iv)(v)(vi) is shrinking the fastest. It is shrinking at a rate of % per year. (d) Which town has the largest initial population (at t=0)? Which town has the smallest?Town (Click for List)(i)(ii)(iii)(iv)(v)(vi) has the largest…In a study of the relation between the expanding budget of an advertisement on a specific product (X) in thousands of pounds and the quantity sold (Y), in tons, of a product. A sample of the advertising budget and the quantity sold in eight successive months is drawn from one of the companies which are dealing in such a product and the following information is obtained.You have conducted a study to determine if there is independence or dependence between market segments (A-C) and prices the segments are willing to pay for a product. The following cross tabular output appears. Under $10 $11-$15 over $15 All A 50 30 20 100 50.00 30.00 20.00 33.33 27.27 50.00 16.67 10.00 6.67 50.00 36.67 13.33 0.000 1.212 3.333 B 40 50 10 100 40.00 50.00 10.00 26.67 45.45 25.00 13.33 16.67 3.33 50.00 36.67 13.33 2.000 4.848 0.833 C 60 30 10 100 60.00 30.00 10.00 40.00 27.27 25.00 20.00 10.00 3.33 50.00 36.67 13.33 2.000 1.212 0.833 All 150 110 40 300…
