Given the joint density function below, solve for the following: 2x +4,0
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![Given the joint density function below, solve for the following:
-2x +3,0 < x < 1,0 < y <1
F(x, y) = 3
0, elsewhere
a. Verify that f(x, y) is a joint density function.
b. Find the P[(X, Y) EA] where A = {(x, y) // < x < 0 < y < } .
c. Find the marginal density g(x) for the joint density function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b107511-84e0-4adc-b7fa-116eaa4646a6%2F56c68b1b-0269-4436-8252-50e2c54f9f24%2F5wnkoev_processed.jpeg&w=3840&q=75)
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- 4. Suppose that the joint distribution of X and Y can be modeled by the following probability density function: S(x, y) = 6x³y, [0, 02. Let the bivariate continuous random vector (X,Y) have the following joint probability density function: {; c 010. Suppose X and Y have a joint density function given by Sca?, for 0< x < y < 1, 10, f(x, y) otherwise. Find c, the marginal density functions, EX, EY, and the conditional expectations E(Y | X = x) and E(X | Y = y).1. Consider the following continuous Joint PDF. x f(x, y) = K.+2 y2 In ½-½The joint probability density of X and Y is f(x, y). Find the marginal density of X at 0.4. The answer should be given to 2 decimal places. g(0.4) = f(x, y)= { 2(x + y) 05.) Suppose the joint density for X and Y is given by f(x, y) = 1/xfor 0 < y < x < 1. Find ρX,YGiven thejoint densityfunction below, solve for the following: a.Verify that f(x, y)is a joint density function. b. Find the P[(X, Y) ∈A]where A = {(x, y) | 1/4< x < 1/2, 0< y < 1/2}. c. Find the marginal density g(x) for the joint density function.d. Find the marginal density h(y) for the joint density function.e. Find the conditional density f(y|x).f. Find the conditional density f(x|y).(1) Find the constant c in the following bivariate density. Scz' y? if z € (-1,1) and y e (x², 1) f(x,y) := if otherwise. The correct answer is 24/7 24 7 4/27 27/4 N/A (Select One)Verify the claim that p (r) = p (x, y) dy, where p(r, y) and p (r) denote %3D the joint density and marginal density, respectively.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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