(a) Find the joint distribution of Y1 and Y2: ƒ (y1, y2) (b) Then compute the marginal density of Y1
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- d, e, fSuppose that consumer has the following utility function: U(X,Y) = X2 + Y2. Which of the following is correct? Preferences are convex and indifference curves are bowed outward from the origin since Law of Diminishing Marginal Utility fails to hold. Preferences are non-convex and indifference curves are bowed outward from the origin since Law of Diminishing Marginal Rate of Substitution fails to hold. Preferences are convex and indifference curves are bowed inward towards the origin since Law of Diminishing Marginal Utility holds. Preferences are convex and indifference curves are bowed inward towards the origin since Law of Diminishing Marginal Rate of Substitution holds.3. Use the method of moment to estimate the parameter 0 for the density f(x;0) I10.01 (x) based on a random sample X1, X2,..., Xm. Give a sufficient statistic for 0.
- The government has set milk prices artificially high at p+ (price/unit). Sketch a graph of a supply curve S(g) and a demand curve D(g). Label the equilibrium price and quantity p* and q*, respectively. Then label a price p+ that is greater than p*. Let qt be the quantity for which the demand curve passes through pt. A. On your graph, highlight the area corresponding to the consumer surplus when the price is pt. This area can be expressed as $0 B. On your graph, highlight the area corresponding to the producer surplus when the price is p+. This area can be expressed as C. The total gains from trade are given by the sum (consumer surplus + producer surplus). How do the total gains from trade change when the price is changed from p* to p+?Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (°F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint density f(x, y) = = { x ² + 30.10. +,0Suppose that the joint distribution function of X and Y is given by f (x, y) =x+y If 0 < x < 1 and 0For x, y ≤ (0, ∞), let X and Y have the joint density 1 -e Y f(x, y) = Y i) Compute the marginal density of Y. ii) Compute the conditional mean and variance of X given Y = y. iii) Compute Var(X).An article in the Journal of the American Ceramic Society, "Rapid Hot-Pressing of Ultrafine PSZ Powders" (1991, Vol. 74, pp. 1547-1553) considered the microstructure of the ultrafine powder of partially stabilized zirconia as a function of temperature. The data are shown below: ... x = Temperature (°C) | 1100 1200 1300 1100 1500 1200 1300 y - Porosity (%) 30.8 19.2 6 13.5 11.4 7.7 3.6 Find an estimate of o2 Input answers up to two decimal places. o2= Blank 1Cont?1) Consider a continuous RV, Y, with a pdf given by f(y)=ce²¹, -∞Suppose X and Y have joint density f(x,y)=10x2y, 0<y<x<1. Find the marginal density of X.Y1 2. Suppose that Y,~ exp(1) and Y2~ exp(1). Let U = Y1+Y2 and V = Y1 + Y2. a. Determine the joint density of U and V. b. Find the marginal distribution of U. c. Find the marginal distribution of V. d. Establish whether U and V are independent.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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