Given the joint density function 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) | 14< x < 12, 0< y < 12}. 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).

Q: d) the conditional pdf of Y given X. e) E(Y|X = -1)

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Q: Find the mass and center of mass of the lamina that occupies the region D and has the given density…

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Q: Let X and Y have the joint density function 1 f(x, y): x > 1, y > 1. Let U = XY and V = 3X/Y. (a)…

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Q: 3. Let (X,Y) have the following joint density function: J ?y? 0<x < 2 , 0< y < 2 f (x, y) otherwise…

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Q: Given the joint density function below, solve for the following: 2x +4,0<x< 1,0 <y <1 F(x, y) = 3 3…

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Q: ... If the joint pdf of (X,Y) is f (x, y) = 6e-2x-3y 9 , x ≥, y0 ≥, find0 the conditional density of…

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Q: Given the function (a) fx.y(x,y): = { b(x + y) [b(x+y)² =2<x<2 and -3<y<3 0 elsewhere Find the…

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Q: What is E(e Y = 1)?

A: First we have to obtain the conditional PDF of X given Y = y to find the required expectation.

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Q: Given the joint density function below, find P(1 <Y<4 |X=1). 8-x-y 0<x<3,3<y<5 f(x,y) = 15 0,…

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Q: Find the density functions fx(x) and fy(y|x) for the joint density function fxy(x,y)=xeXV+I)…

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Q: 1. Hand in: Let f(x, y) = 6y(1 – y), function. Find E(X|Y = y) 0 <x<y<1 and zero eswhere be a valid…

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Q: Let Y have the density function given by 0 <y< 2 f(2) = {-cy", (-су?, 0, elsewhere a. ) Find c. b. )…

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Q: Suppose, we have the joint density of X and Y as fxx (x, y) c(a² + y²); 0 < x < 1,0 < y < 1 = 0,…

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Q: The joint density of X and Y is given by ey f(x, y) = 0 <x < y, 0 < y < ∞. Compute E(X²|Y = y).

A: solution is given below

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A: Given, the joint density of Y1 and Y2 is

Q: E(XY)=?

A: Given Data: f(x,y)=17x2y             for (x,y)=(1,1), (1,2), (2,1)           =0…

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A: From the given information, fx,y=kx+2y, 0&lt;x&lt;1, 1&lt;y&lt;2 The value of k is obtained below:…

Q: 7. The joint density function of X and Y is given by f(x,y) = ze (+1) *> 0, y > 0. Find the density…

A: We have to find out the pdf of product of two random variables.

Q: Given the joint density function below, find P(2<Y<4 | X=1). 9-x-y 0<x<3,3<y<5 f(x,y) = 21 0,…

A: Given the joint density function f(x,y)=219−x−y​  for 0&lt;x&lt;3  and 3&lt;y&lt;5 , and f(x,y)=0…

Q: Find the conditional density of X, given Y = y, and that of Y , given X = x. Make sure to define the…

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