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

Q: a. What value of c will make f(x) a valid density? b. What is P(X = 1)? What about P(X = 1 or X =…

A: The value of c that makes probability density function valid is obtained below: From the given…

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: 2² – 2, a 3 is continuous everywhere. f(z) = O true O false

A: Given: fx=x2-2,  x≤3x+4,  x&gt;3   As we know that; The function will be continuous at x=a when,…

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

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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: Let f(x, y) = and let g(x, y) O O rºy6 26+y6 O 0 0 6x³y³ 6x6 + 6y6 Which of the above functions are…

A: fx,y=x6y6x6+y6if x,y≠0,00if x,y=0,0 gx,y=6x3y36x6+6y6if x,y≠0,00if x,y=0,0

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: 2. Let f(x₁, X2, X3, X4) be the joint density function of (X₁, X2, X3, X 4). Then the joint density…

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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) and let g(x, y) = O O 8xy8 828+8y8 O 3xy6 3x² + 3y¹2 Which of the above functions are…

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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: 4. Let X and Y have the joint density f(x, y) = What is P(X>Y > 2) ? e-(x+y) {"th for 0 ≤ z, y<∞…

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Q: Calculate the work required to lift a 3-m chain over the side of a building if the chain has a…

A: Consider a segment of the chain of length ∆x that has to be lifted x_i feet. To lift this segment…