Let X=(1,0, – 1, -/2)'. Then, ||X||=v2 Select one: True False

Q: 1 Let f (x,y) =In Then f (1, – 1) =... 3x2+4y3 XX

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Q: 10. dr S f(æ) dx = Choose...

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Q: if x~unif. (0,2),find the U.b. of p(lx - mul>= 2)

A: Given X~Unif(0,2) Result: if X~unif(a,b) then  Mean=(a+b)/2 Variance=(b-a)2/12

Q: Evaluate: S, Vte-t² dt.

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Q: 1. Prove that for all x, y ER, max (x, y) = x+y+lx-yl 2 x+y-lx-yl 2 and min (x, y}=-

A: What is minimum and maximum Value: For a given set of numbers, the minimum value of the set is the…

Q: 7. Evaluate. LL sin z da dy.

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Q: 6. Prove that for x > -1 then Vn E N, (1 + x)" >1+ nx .

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Q: y If z = show that = 0. x + y?*

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Q: .Prove that e- -dt < (1+ t²)* 1/4 6.

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Q: If h(x) — За — — 1, j(x) k(x) = 21x? – 26x – 11 , show - 7x + 11 , and - - - - h(x) · j(x) = k(x).

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Q: Prove thiat dx Ś (areten()) ) = し 4+X

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Q: Is it possible to find a number  n  such that is ∫0∞  xn dxconvergent?

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Q: Let Xn ☆ Bil^,p] where n& P ae wnknown. Find method of moments estimators for n&

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Q: Suppose that x̅ = 12, Sx = 2, and z is 1. what is X?

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Q: x*y" + xy'+4y= 2x Ina

A: Cauchy linear differential equation

Q: 2² + e4 z lim z 0 22 – e²

A: This is a form of infinity by infinity so we have to apply Lhospital rule that is differentiate both…

Q: (Superman Versus m ers arrive according uho

A: System 1 Customer arrival rate in a Poisson Process λ Service time  3μ System Capacity…

Q: Let X and Y be independent and distributed as N(u, 1). Is T = X-Y sufficient?

A: According to factorization theorem, If the likelihood function L(x,θ) can be expressed in the form…

Q: az Find for z = x'y'eV

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Q: 2. Z=e Iny

A: Given that, z = ex ln y x = ln (u cos v) y = u sin v We have to fin dz/du and dz/dv. Then we get,…

Q: az Find for z = x²y°e®Y dx

A: The given function z is zx,y=x2y2exy We have to find the partial derivative of z with respect to x.

Q: 2. Determine Var(Y) when Y 3X1 +2X2 with Var(X1) 1, Var(X2) 5, Cov(X, X2) 2, E X1} 3, аnd E{X} 4.

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Q: (4) Evaluate : + yz') dV if Q= {(x, y,z): x:[-1, 1], y:[3, 4], z:[0, 2]}

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Q: (b) f(z) = tan¯"(5z) - (In(2"))®

A: We have to find derivative

Q: 11. Prove that tanh y du = In cosh u + C

A: The integration of the integral is tanhu.

Q: Suppose, X|0~ Binom(m.0)and e- Beta(a,B), then Var (Y) is equals to, maß

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Q: 2. Integrate: S w5 V7+ w3 dw 3. Find S (6-+ - sV) de

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Q: (14) Approximate S, x² ex², Using Simpson's rule dp,

A: Simpson's rule is a numerical method used to approximate the definite integral which represents the…

Q: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

A: The given integral is ∫2 dxx1+lnx2 Find your answer below

Q: dy then In z is If y = cosh z

A: Without wasting any time, any further, differentiate the RHS to get your answer.

Q: Fincd dy for y-sinner} er tot

A: Explanation of the solution is given below...

Q: 11. Prove the absorption law x +xy=x using the other laws in Table 5.

A: To prove: x+xy=x We use the following identities (1) x=x·1 (2) 1+x=1 (3) xy+z=xy+xz    ( This is…

Q: dz Find if yz – In z = x + y ax

A: To find the partial derivative of z of yz-ln z=x+y with respect x, differentiate yz-ln z=x+y, while…

Q: (z In z + 5)dz

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Q: 4. Find two values of c in [-4, 4] such that f(c) is equal to the average value of f (x) = 3 cos 2x…

A: To determine c such that f© is equal to the average value of f(x).

Q: 1. Prove that for all x, y ER, max (x, y) x+y+lx-yl 2 x+y-lx-yl 2 and min (x, y)=-

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Q: Put that: coshx- hel x+Jx=I/,.- cosh x= lml x+J xI/ メン」

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Q: Let Xi- N co,1) and n=2 auel T= Xi+ Xz Show that Tis a %3D Sufficiency Stabisuic Statistic.

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Q: y²

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Q: d 1 Prove that: dz (tan¬1 z) = 1+z?

A: Given query is to find the derivative of the expression.

Q: 10- If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z - x, show that fe fe fe = 0.…

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Q: 12- show that x² J.(x)dx = x²J1(x) + x J,(x) – lo(x)dx

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Q: II z= ě Y x - Juv Find dz dv üs ing chein rule.

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Q: 3. If f(x,y,z)= In 4 xyz Ite t3y:²s²) , find f,,f, and f..

A: Given that: f(x,y,z)=lnxyz4+e-(3xy2z2)

Q: 1 Let f (x,y)=In . Then f „(1, – 1) =...... 3x²+4y3 XX

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Q: Find fCx) if flo)=0 and the tanGat (k,F CX) has ine af Slore x(x+2) a

A: Given for the function F(x), F(0)=0 and tangent line to F(x) at x,F(x) has slope xx2+23.

Q: Show that S ťe dt = 3VI

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Q: Find dr. J (1+z²)3/2 - In Vx² + 1 + x| + In |Vx² + 1 + x| - Ja? + 1 +c Vx² + 1 O Option 3 Option 1…

A: Let I= ∫x21+x232dx Let x=tanθ ⇒dx = sec2θdθ Substituting this in I, we get

Q: Q2-Prove that = va* – x² ify= ()sin () + () va² - x* = va² – x* if y = (;")sin*+ (4) + () Va² - x²

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Q: d'y on of x

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