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

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A: Let's find characteristics of given differential equation.

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A: our objective is to find the required derivative

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A: Here is the solution:

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Q: FIND M'(3) = Page 2 of 4 -1 6 2 g(x) • F(x) LET M (x) = F (g(x)) AND V(x) = 9 (f(x)) 6 FIND V'(3) =

A: Step 1: Step 2: Step 3: Step 4:

Q: 11. 7(t) = (cost, e¹, Int)

A: Given rt=cost,et,lnt We know that dcostdt=-sintdetdt=etdlntdt=1t

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A: Given t~exp(3) It is the standard pdf of exponential distribution with parameter 3.

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A: Laplace transferom

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A: To find the linearization of g(x,y)=tan−1⁡(xy2) at the point (1,1), we willl use the formula for the…

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

Q: Find moment generating function of XY.

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A: Solution: From the given information,

Q: (b) Find Rz (t) in terms of R(t),s SsS

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Q: Find the saddle point/s of the function f(x,y) = x + y² +x²y+4 O a. (E ,-1) & (- 2 -1) O b.(4,0) &…

A: Let's find.

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A: Given:fx=lnx2-3  at a point x=2

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A: Topic -functions qnd average rate of change of function over certain interval

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Q: Show all work! Find the maximum, minimum, and saddle point of f(x,y) = cos(x)+ (1/y^2 + 1/x)+1

A: We will use the basic knowledge of 2-variable calculus to answer this question.

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A: The moment generating function of any function, f(x) is calculated asMXt=∫-∞∞e-txfxdx