Q 6.2. Let X = (X₁, X2, X3)¹ ~ MVN (ux, Ex) where -3 7²) μχ = Compute the distribution of Y and Ex = (a) Compute the moment generating function Mx (t) of X. (b) Compute E(X₁X₂). (c) Let Y₁ Y₂ Y3 = = = 6 -2 -2 - 3X2 X3 + 1 X₁ X₂ X3 X₁ + 2X₂ - 2. (Y₁, Y₂, Y₂)T. -2 -2 2 1 1 1 -

Q: Use the table below to compute h'(-1) for h(x) = f(x) g(). (E) (), (1)6 () 1/2 -2 2 1 -3 1 2 1 4. -1…

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Q: a.) If f(x)= sin(In(x* )), find f'(x). b.) If g(x) = 5x find g'(x). %3D .2 x +3

A: (a) Consider the provided function, fx=sinlnx3 Find the derivative of the provided function. Apply…

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A: GivenP(A'∩B)=0.4P(A∪B)'=0.5

Q: (b). Use the definition of the derivative to evaluate f (x)=x". [Hint: Use the Binomial Theorem:…

A: Given: i. fx=xnii. a+bn=an+nan-1b+nn-12!an-2b2+·····+nabn-1+bn. To Find: Use definition of…

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A: Given: y'(t)= (y-2)(3+y)

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Q: 7 x + 2 Let f(x) = x4 . x + 5 f'(x) = %3D

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Q: Let f(t) = 4t* – 4t + 5e'. Then f'(t) =

A: find the derivative

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Q: a) Suppose that f(4)=3 and f'(4)=-5. Find g'(4) where g(x)=Vx f(x) b) Let y=cosx-sin.x , show that…

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Q: Let F(x) f(f(x)) and G(x) = (F(x))² and suppose that f(3) = 2, f(2) = 2, f'(2) = 2, f'(3) = 14 Find…

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Q: Let f(x)= 1. f'(3)= 2. f'(6)= = 4 VT Evaluate each of the following:

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A: Answer: Using the given data,

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A: The moment-generating function f(x) where 0&lt;x&lt;1

Q: Let 7(t) = Find 7'(t) 7 (t) =

A: Topic - vectors and derivatives Since r→t = 5 t5-1, -e-t, -3 sin2t we to find r→'t  derivative of tn…

Q: Let f(x) = In[x4(x +9)6(x2 + 4)3]. Find f'(x). f'(x) =

A: Given,

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Q: let p(x)=g(f(x)). use the given table to find p'4

A: p(x)=g[f(x)] diff. w. r. to x p'(x)=g'[f(x)] . f'(x)  ..................(1)

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Q: Q4 (40 points): x' = x + -2 x(t) = ? %3D

A: The objective is to find the value of xt given that  x'=3-22-2x+12e-t

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A: Given that,

Q: - 3 Let f(x) = 8xVæ + x2. f'(x) =

A: Use the derivative for finding the answer.

Q: Find given that y=[atan-¹(bx)]². dy dx Assume a,b ER. 2[atan-¹(bx)] O 2[atan-¹(bx)]- O 2b[asec²(bx)]…

A: To find dydx given that y=a tan-1bx2.Assume a, b∈ℝ

Q: Let F(2) = 2, F'(2) = 3, H(2) = 4, H'(2) = 3. A. If G(z) = F(z)*H(z), then G'(2) = _______ B. If…

A: The Product Rule:The Quotient Rule:

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Q: Suppose f(x) = [ 6t² /1+t° dt .

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Q: 4) Knowing that f = f(t), using the expressions of L[f'] and L[f"], derive an expression for d'f…

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Q: (b) Verify mean value theorem for f(x)=x² - 5x+6 over the interval [1,3].

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Q: Let 7(t) = Find 7'(t) F'(t) =

A: The objective is to find the derivative of given

Q: Show that -E{t, log(sigma(w*x)) + (1 – t;) log(1 – sigma(w"x;))} = E, log(1+ e-yw* x %3D Where…

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