Find E(Y/X) for the density function #(1+3y²). 0 < x < 2, 0 < y < 1 4 f (x, y) || 0, elsewhere.

Q: Suppose X1 and X2 have joint density function { fx,,x2 ("1, #2) 0, O.W. E[X1]E[X2] Find the marginal…

A: GivenJoint density functionfX1,X2(x1,x2)=1πx12+x22≤10otherwise Let us say X1 range from -1 to 1,…

Q: 3. Determine the constant a so that f(x) is a valid density function. - f(x) = {a(3 — x²), a) 0.3333…

A: Ans#- Given, f(x) is valid density function           f(x) = a(3 - x2)-1 ≤x≤10otherwise…

Q: e /// 2 Evaluate 2xz dV where E {(x, y, z) |1 ≤ x ≤ 4, r ≤ y ≤ 2r, 0 <z<x+3y}

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Q: 0<x<2; 0<y<1 f(x, y) = x(1+3y²) 4 0 otherwise a) Find the marginal densities of X and Y. b) Find the…

A: Given f(x,y)=x(1+3y2)/4  0&lt;x&lt;2; 0&lt;y&lt;1

Q: Let Z ∼ N(0,1) and Y = Z1/3 (a) Find the density function (pdf) of Y . b) FindP (Y> (1/4)^1/3))

A: Given:- Let Z ∼ N(0,1)  Y = Z^1/3

Q: So If fis continuous and f(x) dx = 20, evaluare let U = 3x f² f(3x) dx.

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Q: Suppose you choose a real number X from the interval [2, 10] with a density function f(

A: Given that the density function for X is, fx=148x, 2≤x≤10

Q: Let f(x, y, z)= exy sin(x+y) Calculate fxxz· z²+1

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Q: Astroid: (0 s t s 2x) x = a cos3 t y = a sin3 t a ab 3 o 2ra2 O zab 2nab

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Q: 8. Show that the gamma density function f(x, λ, r) integrates to 1

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Q: Suppose that X and Y have a joint density function given by e-(a+y)r,y> 0, otherwise f(x, y) (a)…

A: From the provided information, the joint density function is,