a) Find a constant b>0 so that the function 5x f,(x) = e 6 ; 0

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Q: 3. The density function of X is given by f(2) = {"* + bx? 0sxs 1 otherwise If E[X] = ; find a and b.

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Q: O Let X' and 'Y' have a joint density function 0<x< 1,0 < y< 1 other wise

A: Given information: The joint density function of the random variables X and Y is as given below:

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

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Q: Suppose that the unit cube E = [0,1]3 in R3 has a constant density function. What is the center of…

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Q: Let Y, and Y2 have a joint density function given by fG) = [3y1 0<y2 < yı <1 to, 10, elsewhere.

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

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Q: Q5) If X and Y have the joint density function Li + xy 0 < x< + dx).

A: It is given that X and Y have the joint density function fx, y=34+xy, 0&lt;x&lt;1 ; 0&lt;y&lt;10…

Q: (a) Let Z = vX. Show that the density function of Z is given by %3| (-). fz(z) = 2a exp z > 0.

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Q: (a) Find a constant b' (in terms of 'a') so that the function fyy (x, y) = b e (*+ y) for 0 <x <a,…

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Q: 2 a- If the continuous RV X has Rayleight density f(x) = a? x U(x), find E(X") and deduce the values…

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Q: A

A: Given: p(x) = x^2+5x

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Q: 4. The joint density function of X and Y is given by 4y if 0 < x < 1,0 <y <x² f(r, y) = 0.…

A: First we figure out the marginal density fxx  of X.Now,  ∫0x2 fx,y  dy=∫0x24yx3 dy=4x3.y220x2…

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Q: Let X and Y have the joint density function 0<x<1; 0<y<x, 2, f(x,y)= 0, Otherwise. Calculate E(XY).

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Q: If the joint density function of X and Y Is given Sk(x+2y), 0 <x< 1;1<y<2 0, elsewhere f(x,y) = a.…

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: Suppose that the unit cube E = [0, 1]3 in R³ has a constant density function. What is the center of…

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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: Q3- If the density function of X is 0 <x < 4 (x) = 38 0.w Find the probability mass function of Y =…

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Q: 4. Let X and Y denote the lengths of life, in years of two components in an electronic system. If…

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

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Q: (a) Find the constant 'b' such that this is a valid joint density function. (b) Determine the…

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Q: 1. Compute E[X] and Var(X) if X has a density function given by Gxe-x/2 x > 0 (0, otherwise a. f(x)…

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Q: Find the mass of the thin bar with the given density function. 2 p(x)=x√ 16-x; for 0≤x≤3

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Q: The joint density function of X and Y is given by C· x? for x, y > 0, 4.x2 + y? < 1, f(x, y) = 0. ||…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: - If the density function of X is (2x (x) = } 9 0 < x < 3 0. w Find the probability mass function of…

A: Given that Y=X [floor function]This means Y=0 when 0≤X&lt;11 when 1≤X&lt;22 when 2≤X&lt;3So…

Q: Find the mass of a thin bar with the given density function p(x) = 1 + cos x, for 0<xs T/2 %3D

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