1.5 Solve the below problem: Let Y, and Y, have a joint density function given by fU1, 92) = (3y1 0< y2 < y1 < 1 elsewhere. The marginal density function for Y, is f(y2) = (1– y3), 0 < y2 < 1. Find the marginal density function of Y,. (NB: Show all your calculations)

Q: 9. Find the characteristic functions of the following density functions: (a) f(x) = ex for x € R,…

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Q: et (X, Y)' be a random vector with the following density function: (8xy ifosasysl elsewhere ind the…

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Q: 9. If X, Y have some bivariate density, prove that Var(X – Y) = Var(X)+Var(Y) – 2Cov(X,Y).

A: We have given that X and Y are random variables having some bivariate density.

Q: otherwise (f) Calculate E(X). 1.3333 (g) Calculate V(X) and o V(X) (h) If the borrower is charged an…

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Q: Let (X,Y) have the joint density function f(x,y) = { (6/5)(1+x+y) for 0 s x, y s 1, x+ys1 otherwise…

A: Given the joint density function of (X,Y) as fx,y=651+x+y     for  0≤x,y≤1 , x+y≤1         0…

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A: From the given information, Given that   f(x)=0.5x    ;     0&lt;x&lt;2 That is f(x)=12x

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A: Given that  The joint probability mass function of X and Y is  P(x,y)=1/18(2x+y).        for x=1,2…

Q: Let (X,Y) have the joint density function f(x,y) = { (6/5)(1+x+y) for 0 < x, y < 1, x+y<1 otherwise…

A: From the given information, fx,y=651+x+y, 0≤x,y≤1, x+y≤1 g) Consider, fx=∫yfx,ydy…

Q: 2.6 Solve the below problem: Let Y, and Y2 have joint density function Se-Os+y2), f(y1»Y2) = {{o, Yı…

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Q: Let Y possess a density function f (y) = c(2 − y),                        0 ≤ y ≤ 2,        0,…

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Q: There are two components in an electronic system. Let X and Y denote the lengths of life in years.…

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Q: (7) Find the marginal density of X when the conditional density of X given {Y = y} is Poisson(y) and…

A: 7. Note that X|Y=y is a discrete distribution and Y is continuous distribution. Given, X|Y=y ~…

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Q: Let fi(x) and f2(x) be two density functions on (-o, 0). Prove fi(x)log(2))dx < 0 $2(x).

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Q: 3y, 0sysys1, Suppose that the joint density function for Y, and Y, is given by f(y,,Y2)={ Otherwise.…

A: Introduction: The joint density function for Y1 and Y2 is given by,

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Q: 5. The joint density function is given by | 30xy², x-1 0| X = 0,75).

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Q: Suppose a beam lies along the interval [0, 2] on the x-axis and has variable density o(x) = 3 + 2x –…

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Q: Let A > 0. Suppose (X, Y) has joint probability density function given, for all x, y E R, by 3. fx.x…

A: Given that  Let X and Y has joint probability density function :  We have to find marginal…

Q: ave a joint density function given by (3y1 0s y2 s yı <1 elsewhere. lensity function for Y, is f(y2)…

A: *Answer:

Q: Calculate the mass of the straight wire from x = 0 to x =, where as the density function is p(x) =…

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Q: Consider the joint density function 1, f(x, y) = 10, Compute the correlation coefficient pxy. x>2,…

A: The given joint pdf of (X,Y) is as follows,  f(x,y)=16yx3 ,2≤x,0&lt;y&lt;1