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- 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 isIfX1 andX2 are the means of independent random samples of sizes n1 and n2 from a normal population with the mean μ and the variance σ ^2 , show that the variance of the unbiased estimator ω·Xbar1+(1−ω)·Xbar2is a minimum whenω=n1/(n1+n2)Q3 - Returns on stocks X and Y are listed below: Period 1 2 3 4 5 6 7Stock X 3% -2% 9% 6% -1% -4% 11%Stock Y 1% -4% 7% 12% 3% -2% -1% Consider a portfolio of 20% stock X and 80% stock Y. What is the (population) variance of portfolio returns? Please round your answer to six decimal places.
- Q3 - Returns on stocks X and Y are listed below: Period 1 2 3 4 5 6 7Stock X 5% 6% -2% -4% 6% 10% 7%Stock Y 1% -3% 6% 3% 12% 7% -5% Consider a portfolio of 40% stock X and 60% stock Y. What is the (population) variance of portfolio returns?Please round your answer to six decimal places.Where did we get the one over two-squared? I don't understand why it is one over 2^2 Variance (Px+Py).A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.33. A dietician is asked to test this claim and finds that a random sample of 24 servings has a variance of 1.37. At α=0.01, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. Complete parts (a) through (e) below. (a) Write the claim mathematically and identify H0 and Ha. A. H0: σ2≤1.33 (Claim) Ha: σ2>1.33 B. H0: σ2≠1.33 Ha: σ2=1.33 (Claim) C. H0: σ2≥1.33 Ha: σ2<1.33 (Claim) D. H0: σ2=1.33 (Claim) Ha: σ2≠1.33 (b) Find the critical value(s) and identify the rejection region(s). The critical value(s) is(are) enter your response here. (Round to two decimal places as needed. Use a comma to separate answers as needed.) Choose the correct statement below and fill in the corresponding answer boxes. A. The…
- (a) In each Australian capital city, a large retail chain has several stores, including in Brisbane and Perth. An analysis of the variations in profits from each of these cities indicates that the variance of monthly profits in Brisbane is about 2570(k$)^2 and the variance of monthly profits in Perth is about 1789(k$)^2 . A comparison of the difference in profits between the two cities indicates that the variance of the monthly difference in profits between these cities is about 1253(k$)^2 . (i) Calculate the covariance between the two cities' monthly profits using this information. (ii) Find the correlation (ρ) between the monthly profits in these two cities. (b) Quality control staff wish to estimate what proportion p of the resistors made in their factory are scrapped due to defects. Based on a random sample of n = 750 resistors from the production line, they calculate the scrapped resistor proportion to be ˆp = 0.016. Use this information to determine an approximate range a. This…(a) In each Australian capital city, a large retail chain has several stores, including in Brisbane and Perth. An analysis of the variations in profits from each of these cities indicates that the variance of monthly profits in Brisbane is about 2570(k$)^2 and the variance of monthly profits in Perth is about 1789(k$)^2 . A comparison of the difference in profits between the two cities indicates that the variance of the monthly difference in profits between these cities is about 1253(k$)^2 . (i) Calculate the covariance between the two cities' monthly profits using this information. (ii) Find the correlation (ρ) between the monthly profits in these two cities. (b) Quality control staff wish to estimate what proportion p of the resistors made in their factory are scrapped due to defects. Based on a random sample of n = 750 resistors from the production line, they calculate the scrapped resistor proportion to be ˆp = 0.016. Use this information to determine an approximate range a. This…A finance analyzer have come to the conclusion that he wants to purchase stocks from Company A, with an expected yield of E(X) = 4% and variance to the yield being V(X) = 0.49. Another stock from another Company B have an expected yield of E(Y) = 6% and variance V(Y) = 0.64. The correlation of the yield between the two stocks is p(X,Y) = 0.3. The finance analyzer wants to invest a portion p(0 < p < 1) into Company A stocks, and the rest (1 - p) into company B stocks. The combined investment have a yield of W = pX + ( 1 - p)Y. For p = 0.4, such that W = 0.4X + 0.6Y. What is the expected value and variance for W.
- 2) Let G and H be two independent unbiased estimators of θ. Assume that the variance of G is two times the variance of H. Find the constants a and b so that aG + bH is an unbiased estimator with the smallest possible variance for such a linear combination.A chemical supply company currently has in stock 100 lb of a certain chemical, which it sells to customers in 4-lb batches. Let X = the number of batches ordered by a randomly chosen customer, and suppose that X has the following pmf. x 1 2 3 4 p(x) 0.3 0.5 0.1 0.1 Compute E(X) and V(X). E(X) = batches V(X) = batches2 Compute the expected number of pounds left after the next customer's order is shipped and the variance of the number of pounds left. [Hint: The number of pounds left is a linear function of X.] expected weight left lb variance of weight left lb2The management of a supermarket wants to adopt a new promotional policy of giving free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditure for all customers at this supermarket will be normally distributed with mean 400 L.E and a variance of 900 L.E2. 1) If the management wants to give free gifts to at most 12% of the customers, what should the amount of expenditure be above which a customer would receive a free gift? 2) In a sample of 100 customers, what is the number of customers whose expenditure is between 420 L.E and 485 L.E? 3) What is a probability of selecting a customer whose expenditure is differ than the population mean expenditure by at most 50 L.E? 4) What is the percentage of customers whose expenditure is at least 450 L.E.?