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2. Let X = (21) have a bivariate normal distribution with mean vector Air and covariance matrix 1 2 po102 Er = X2 po102 03 If we form y = (exp(1)), then y has a bivariate log-normal distribution. . a. How do you generate an observation for X1? . b. How do you generate from a bivariate log-normal distribution with mean ly = (2) and covariance matrix yl y2 y1 16 4 S, = y2 4 92. Contour of bivariate Gaussian. Sketch the contour defined by f(x, y) = 0.06, where f(x, y) is the bivariate normal density with (a) Ax = 1, My = 2,02 = 03 = 1 and pry = 0. (b) Hz = 0, My = 0, 03 = of = 1 and Pry = 0.2. (c) #x = 0, My = 0,02 = 07 = 1 and Pxy = 0.8. (d) Ax = 0, My = 0,02 = 4, 0% = 1 and pry = 0.8. Here, o2 := VarX, o2 := VarY, and the correlation coefficient is defined as Pry := E(X -HI) ( Y-Hy) What is the distribution of X - Y, when (X, Y) has each of the bivariate distributions given above?2. Contour of bivariate Gaussian. Sketch the contour defined by f(x, y) = 0.06, where f(x, y) is the bivariate normal density with (a) Ax = 1, My = 2,02 = 03 = 1 and pry = 0. (b) Hz = 0, My = 0, 03 = of = 1 and Pry = 0.2. (c) #x = 0, My = 0,02 = 07 = 1 and Pxy = 0.8. (d) Ax = 0, My = 0,02 = 4, 0% = 1 and pry = 0.8. Here, o2 := VarX, o2 := VarY, and the correlation coefficient is defined as Pry := E(X -HI) ( Y-Hy) What is the distribution of X - Y, when (X, Y) has each of the bivariate distributions given above?OPPORTUNITY COST WORKSHEET 2 Below, you are provided Gerardo's Production Possibilities Frontier between biology homework and economics homework before and after he attends economics tutoring sessions. You will use this information to identify how a technological innovation that affects production of only one good alters the opportunity cost associated with producing both goods. PPF1 depicts Gerardo's PPF between biology homework and economics homework before he attends economics tutoring sessions. PPF2 depicts Gerardo's PPF between biology homework and economics homework after he attends economics tutoring sessions. 14 Economic Homework (in pages] 10 12 14 Minlazy Homework [in pages) Part 1: Before Gerardo attends economics tutoring sessions, what is his opportunity cost of producing an additional page of economics homework? Part 2: Before Gerardo attends economics tutoring sessions, what is his opportunity cost of producing an additional page of biology homework? * Part 3: After Gerardo attends economics tutoring sessions, what is his opportunity cost of producing an additional page of economics homework?A consumer receives an endowment of $600.00 this period and $300.00 next period. Currently the interest rate is 20.00%. The present value of the endowment is $ 850 The future value of the endowment is $ 1020 Part 2 (1 point) See Hint Suppose that instead, the endowment is $720.00 in the current period and $300.00 in the next period. Which of the following statements is correct? Choose one: A. Because the current income is higher than before, the budget constraint must be flatter than before. O B. The budget constraint is neither steeper nor flatter than before. O C. Because both the present value and the future value of the endowment have changed, the budget constraint must have different slopes left of the endowment point and right of the endowment point (that is, the budget constraint must be kinked at the endowment point). D. Because the current income is higher than before, the budget constraint must be steeper than before
