Let the two continuous RV X, Y have joint PDF 2 : 0

Q: let w=ln(x2+y), x= 2t, y=4-t. compute dw/dt a) using the Chain rule, draw corresponding tree diagram…

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Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4).…

A: our objective is to find the required derivative

Q: Let f:A-B and X,Y be subsets of B. Then f-¹(XnY) = f'(X) nf-¹(Y). True False

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Q: Let X ~ N (0, 1). Demonstrate that E (X)=0 and V (X)=1.

A: To demonstrate that E(X)=0 and V(X)=1 for a standard normal distribution X∼N(0,1), we need to…

Q: (d) Are X and Y independent? Justify your answer.

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Q: J(u) = [ (x2 + u(t)²)dt min s.t. dri = 12 dt dr2 dt T1(0) = r2(0) = 0 x1(1) = 1 and r2(1)…

A: As per the question we have to find the optimal control law u* , which minimizes J(u) And we will…

Q: Let f(2) = In[="(= + 7)*(z² + 7)°] f'(x) =

A: Given : fx = lnx8x+72x2+76

Q: 11. Let X, Y, Z have the joint PDF f(x, y, z)= 6(1+x+y+z) 10 Find the PDF of U=X+Y+Z. if 0 < x,0 <y,…

A: To find the PDF of U = X + Y + Z, we will use the method of transformation of variables. First, we…

Q: Evaluate 2æz dV where E = {(x, y, 2) | 2 < * < 3, z < y < 2x, 0 < z< z + 2y}

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Q: sume that f(t) is continuous on [a, b| and that u = g(t) is cont ferentiable on [a, b], then f(u)…

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: -If F= 3xyz' i+ 4x'y} – xyzk the find V (V-F) and V × (V × F) at (– 1,2, 1). Also verify that V…

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Q: Let X~U (0,0), then P(X > X²) is

A: Given that X~U0,θ fx=1θ-0=1θ, 0≤X≤θ

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: et g(x, y) = In x + 2 In y - x-8y . Find the critical points. use the second Derivative Test to…

A: g(x, y) = In x + 2 In y - x-8y

Q: If f(x,y,z) = e* and g(x,y,z) = y – z Then, V (fg) will be;

A: Given fx,y,z=ex, gx,y,z=y-z

Q: 4. Let f(x, y)=2x*y' . Find f,(x,y)

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Q: Let f(t) be a continuous function with f(0) 5 and f(4) = 3. Compute F'(2), where cx² F(x) = [" .…

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Q: Suppose that f is a continuous function satisfying stæ) = a f(t)dt + * So f(t)dt + a %3D for all a,…

A: Solve the function

Q: 6. Show that f(x) = sin x is uniformly continous on R.

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Q: Let f(x) = sin? (x). Define F(x) | f(t) dt. What is F" -) ?

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Q: The joint pdf of Y, and Y, is given by (a) ,with support (b) , and 0 elsewhere. (a) 1/y2; (b) 0 < y…

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Q: (3) Determine the values of a for which x4 + y* , if(x, y) # (0, 0), (x² + y?)ª f(x, y) = ,if(x, y)…

A: solution.

Q: 11. The function f(x) is defined on [1, o0) and satisfies VTO dt. 10 Find f(x).

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Q: The Boolean function F(x, y) = x'y + xy' + (x+y')x can be simplified to:

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Q: Let f(x, y) = e-o-Y 0 < x < ∞, 0 < y < ∞ be the joint pdf of X and Y. Find the pdf and cdf of X and…

A: The joint probability density function is given as below: f(x,y)=e-x-y ; 0&lt;x&lt;∞, 0&lt;y&lt;∞

Q: 9. Explain why dt r1/I dt 1+t2 1+t? is valid for any x > 0.

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Q: 6. If f(x,y) = 2 x>0; y>0; x+y<1 Show the conditional pdf of Y given x is uniform.

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Q: Let i, j, k e Za and w, x, y e Zb with i, j, k all different from each other and w, x, y all…

A: Let the number of elements in the domain be equal to m, and the number of elements in Zb be equal to…

Q: 3. Prove F (Vr)(A→ B) → (Vx)A → (Vx)B. ->

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Q: 3. X is N(5,9). Obtain the pdf of Y=3X-5 and Z=5-X.

A: The X is N(5,9).Know that if X is normally distributed then the PDF of X isWant to calculate the PDF…

Q: The moment generationg function of X is defined by M(t) =Var(etx) ylgn ihi

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