LET (X,Y) be a two-dimensional continuous v.a, with density f(x)=x(x+cy), 0

Q: R (T) is bounded by its value at the origin i.e., IR, (t)l<Rxx (0) XX XX

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Q: Let f: R² R2, f = (f1, f2), be defined by f(0,0) = (0,0), and y³ 23 x² + y²¹ f₂(x, y). x² + y² (a)…

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Q: The joint pdf of X and Y is given by fx,y(x,y) = {4x2   0<y<x<1}…

A: Sol:- To find the support of U, we first need to find the range of values that U can take

Q: f(x, y) = 1 – |ry|l a.) Is f continuous at (0,0)? b.) Is f differentiable at (0,0)?

A: Given f(x,y)=1-|xy|   a. i. Let approach (0,0) through the y-axis 1-0= 1  2. Lets approach (0,0)…

Q: Is the following bounded or unbounded and why? f(x,y) = ln(x2 + y2)

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Q: 1 Let f (x, y) =x²y*sin (- x²+y* when (x, y) ± (0,0) and f (0,0) =0. determine if f is continuous in…

A: We have to show given function is continuous at origin

Q: If X, Y have some bivariate density, prove that Var(X – Y) = V ar(X)+Var(Y) – 2Cov(X,Y). | (justify…

A: The objective is to show var(x-y)=var(x)+var(y)-2 Cov(x,y)

Q: 3r²y Determine if ƒ is continuous at (0,0) where f(r, y) = { r4 + 2y2 (x, y) + (0,0) (1, y) = (0,0)

A: for f(x) to be continuous at (0,0) limx→0+,y→0+f(x,y)=limx→0-,y→0-f(x,y)= f(0,0)

Q: Assume that f(r, y) is a function given by f(x, y) = x² + y² + x?y+4 %3D on a bounded domain D =…

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Q: - The spectral density of a process {X(t)}, real or complex, is a real function of w and non…

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Q: Let X =ela, b), spoce of all continuous function defined on fa, b] Find diameter of X , dia (X) =…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 1. Let X, Y, Z have joint pdf f(x, y, z) = 2(x + y + z)/3, 0<x< 1, 0 <y< 1,0 < z < 1, zero…

A: Answer: - Given, X, Y, Z have joint pdf                 f(x, y, z) = 2(x + y + z)3 ,  0 &lt;x &lt;3,…

Q: 2. Let X and Y have the joint density (Cx²y if 0 < x < y < 4 f(x) = %3D otherwise a) Find the value…

A: Given: The joint density function of X  and Y is given as:…

Q: Prove that if f is continuous, then f(t)(x-t) dt = f(u) du ) dt

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Q: Let g(x, y) = x4 + y² – 4x³ + 5x – 6y+3. Show that g(x,y) continuous (actually at least aC')…

A: Recall [ Implicit Function Theorem ]

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

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Q: (0 if xE Q (1 if x E I If f (x) = show that f is not Reimann Integrable

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Q: Let f(x, y) = sin (x - y) [x] + [y] ' 0, |x | + (x, y)

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Q: 1) Let f(x,y) = 6x,0 < x < y<1 and 0 elsewhere. Find a) The marginal density of X and Y

A: The provided information is  f(x,y)=6x    0&lt;x&lt;y&lt;1   and 0 otherwise Therefore  a. The…

Q: r(t) = ti +j+ tk is continuous at t = 0. اختر احدى الدجابات True False

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Q: Find h(x, y) = g(f(x, y)). h(x, y) = g(t) = t² + √t, f(x, y) = 4x + 5y - 20 Find the set of points…

A: The square root function  is always continuous , when

Q: If f (x) = c (9 – x²) for 0 < x < 3 is a density then c is equal to

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Q: Let f : R? → R given by f(x, y) = for (x, y) # (0,0) x4 + y? and f(0,0) = 0. Is f continuous at…

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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: f(2) = u(x, y) + jv(x, y) v(x, y) = sin x cosh y f (0) = 0.

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Q: EXAMPLE 2 The set {sint, cost} is linearly independent in C[0, 1], the space of all continuous…

A: The given set is sin t, cos t.We need to show that the set is linearly independent.

Q: Find continuous functions

A: Given,        fn:0, 1→[0, ∞)