1. Let f(x, y) = where C is a constant. (x2 + 1)(y² + 1) ’ For which value of C is ƒ a joint density function?

Q: Let f (L, K ) = 32LK. Find df/dL.

A: Differentiate the function f with respect to L.

Q: Isin , it (z, y) # (0, 0) 2. Determine if a function f : R → R defined by f (r, y) = 0, if (z, y) =…

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Q: D. On what point/domain will the f(x, y) = Vx ey will be continuous? Explain your answer!

A: Solved below

Q: z = f(a + y, 2ry) f we take u = x' + y' and w = 2xy we obtain z, = 2xf, + 2yf, and z, = 2yf, + 2xf.,…

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Q: Let f(x,y) = cx2y, x2<=y<=1, -1<=x<=1 be the pdf of X and Y. Find the value of c that makes this a…

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Q: Assume that d and e are constants and, 3 - f, if f <1 {. z(f) = df² + ef, if f < 1

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Q: Suppose f is a differentiable function of x and y, and g(u, v) = f(e" + sin(v), eº + cos(v)). Use…

A: Given: f is a differential function of x and y . gu,v=feu+sinv,eu+cosv         Objective is to…

Q: a) Find the gradient of f(r, y, z) = e2= sin(2x)cos(2y)

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

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Q: 1. Let f(u, v) be a continuously differentiable function. Let u = e*, v = e³. Show that u²fuu + v²…

A: Given that f(u,v) is a continuously differentiable function, and u=ex, v=ey then show that…

Q: alculate D(f ◦ g) for the fun

A: answer is in next step

Q: Let X and Y have the joint pdf f(x, y) = (1 –- xy), 0 < x < 1, 0 < y < 1. Find V(X).

A: let X and Y have the joint pdf f(x,y)=43(1-xy),   0&lt;x&lt;1, 0&lt;y&lt;1 marginal density function…

Q: Let x = s + t and y = s - t. Show that for any differentiable functionf (x, y),

A: Given: x=s+t and y=s-t and a differentiable function fx,y To show: ∂f∂x2-∂f∂y2=∂f∂s∂f∂t,