Find the marginal densities of X and Y using the joint density fxy(x, y) = 2u(x)u(y) exp = 2u(x)u(y) (1) Exp[-(4x + 1)]
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Q: 7.Find the value of k if f (x, y) = k(1- x)(1- y) for0 < x, y < 1 is to be joint density function.
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![Find the marginal densities of X and Y using the joint density
fxy(x,y) = 2u(x)u(y) exp
v>exp[-(4y + 4)]
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- the joint pdf of X, Y is given byIf (Y(t)} is the square law detector process and if Z(1) = Y(t) – E{Y(t)}, show that 1 the spectral density of {Z(r)} is given by S„@) : | S@) S„(@- a) da, where S,(@) is the input spectral density.Suppose that an automobile dealer pays an amount X (in thousands) for a used car and then sells it for an amount Y. Suppose that X and Y have the joint density fxy (x, y) = for 0 < x < y < 6. The dealer's expected profit (in thousands) from the sale is equal to
- Let X, Y have the joint density function 2 \exp(-x-y) if Are they independent? Find Cov(X,Y). 0Calculate cov(X,Y)What is the partial derivative of V with respect to S?5) For the following density function f(x) = c x2 (1–x), 0Now, assume that Y₁,..., Yn distributed iid, each with density -{* where is positive constant. Find the density function for fy) (y). fy(y) = e-(-0), 0, if y> 0; otherwise,#2, Suppose that X and Y have joint density given by: f (x, y) = 15x²y, 0 < x < y < 1. (a) Find the marginal pdf of Y. (b) Find the conditional pdf of X given Y. (c) Find the conditional expectation of X given Y = 1/3. (d) Are X andY independent? Show this in two different ways. (e) Give an integral expression for P(X + 2Y < 1), but do not evaluate it.SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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