3.41 Show that the Neumann problem v²u = 1 in r+ y<1 au D2 on x+ y 1 does not have a solution.
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- 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 linear model Yi = B0 + B1X1i + B2X2i + ui where ui is the error term and where E(ui|X1i,X2i) = 0, observations (Yi,X1i,X2i) are independent and identically distributed, 0 < E(Y4) < 1, 0 < 1i E(X14i) < 1, 0 < E(X24i) < 1 and where X2i = X12i. Are the OLS estimators Bˆ1 and Bˆ2 of the coe¢cients B1 and B2 unbiased and consistent? Explain.SO what would be the L, Lq, and Wq of this problem? Assuming we are trying to develop and sovle a waiting line system that can accomodate this increased leel of passenger traffic.
- If the t-computed value is 2.115 and the critical value is 2.423, what will be the decision? a. Reject the null hypothesis. b. Do not reject the null hypothesis. c. Reject both the null and alternative hypotheses. d. Support both the null and alternative hypotheses.*A Consumer is willing to trade 3 unit of x for unit 1 of y ,when she has 6 unit of x and 5 unit of y.she also willing to trade in 6 unit of x for 2 unit of y,when she has 12 unit of x and 3 unit of y.she is indifferent between bundle (6,5) and bundle (12,3).what is the utility function of for goods x and y? hint: what is the shape of indifference curve?*Use complementary slackness and the solution to its dual problem to find solution(s) to the primal LPP.
- Suppose that 2 balls are randomly selected (without replacement) from an urn containing 3 red, 4 blue, and 5 white balls. If we let X and Y denote, respectively, the number of red and white balls chosen. a) Solve for P(x=0, y=0) b)Solve for P(x=1, y=2) c)Solve for P(x=2, y=1)Suppose that 2 balls are randomly selected (without replacement) from an urn containing 3 red, 4 blue, and 5 white balls. If we let X and Y denote, respectively, the number of red and white balls chosen. Solve for P(X=2).Determine the least squares solution to Ax = b, where
- 2. Solve using Gauss Jordan Elimination Method. Compute also for x, y and z.Two different types of polishing solutions are being evaluated for possible use in a tumble-polish operation for manufacturing interocular lenses used in the human eye following cataract surgery. Three hundred lenses were tumble polished using the first polishing solution, and ofthis number, 253 had no polishing-induced defects. Another 300 lenses were tumble-polishedusing the second polishing solution, and 196 lenses were satisfactory upon completion.(a) Is there any reason to believe that the two polishing solutions differ? Use α = 0.01Write down the R solutions of the following questions. Two types of medication for COVID-19 are being tested to determine if there is a difference in thepercentage of adult patient reactions. 20 out of a random sample of 200 adults given Medication_Astill had COVID-19 30 minutes after taking the medication. 12 out of another random sample of 200adults given Medication_B still had COVID-19 30 minutes after taking the medication. Test theequality of proportions at a 1% level of significance.