Show that Var (XY) = X²Y²- (XY)² provided. X and Y statistically independent.

Q: Evaluate the integral dx 2x x - 3x? 1 V3 + V2 x u- - V7 VX + C 2/3 TV3 1 In 2/3"/7x + V3 +C -In 4…

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Q: 5. Evaluate the integral 2 c2x x2 (x² + 2y³) dy dx.

A: As per bartleby guidelines we are supposed to answer only one question per post. This post contains…

Q: 2- Suppose = {xt)dt . Find ES and d acconding the statistical characteristics of xt).

A: For a continuous random variable X, a probability density function is a function such that (1) f(x)…

Q: Find the maxamin s in flectlon Points and the in ter Vals on which the function inerease,decrease…

A: follow the solution which is mentioned in step 2.

Q: 7 Find the most general antiderivative for the function – 5VP. 2 -

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Q: how do you find z sub alpha over 2 using table a-2

A: I am solving this question by taking an example Let us take α = 0.05 We need to find

Q: find integral x3 3) S dx /1-x²

A: We have to find the indefinite integral

Q: Find the equation of the normal line (NL) to the graph f(x)=x³ – 4x atx = 3 .

A: We need to find derivative.

Q: Evaluate L 8y (x³ + 1)² 2y by reversing the order of integration. dady

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Q: a. Determine the marginal p.d.f.'s of X and Y. b. Are X and Y independent? c. Are the event (X 1/2}…

A: It is asked to find the marginal pdf's of X and Y. Marginal pdf of X. fx(x) = ∫0132y² dy=32∫01y²…

Q: Evaluate J S S dydx. r4x Jx2

A: To solve this question first integrating with respect to y and plug in the limit then integrate with…

Q: # 13) Find two positive numbers x and y for which 2x +y = 30 such that xy² is maximized.

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Q: 1,3 2,1 3,4 f(x) 2,6 3,5 3,2

A: The given tabular data is,

Q: Find the simplest integrating factor u(x) of - xy' = (8x + 9)y + x In(x). µ(x) = %3D

A: As the given equation is an first order differential equation ,we can find integrating factor.

Q: Suppose you estimate the following regression function where Y, X1, and X2 are continuous variables…

A: The following solution is given below :

Q: Find the total differentials of w=2z2 ysinx

A: The detailed solution is given below Thank you

Q: A system consists of two components whose lifetimes (in years) X1, X2 are inde-pendent and…

A: a) The expected value of x can be calculated as follows:

Q: X₁ and X₂ are random samples from exp(). when x > 0.) (pdf of exp()=e Determine the constant c so…

A: we have given that Xi follow exponential with mean λ that is E(Xi) = λ also, X1 and X2 are…

Q: The joint and marginal pmf's for X = automobile policy deductible amount and Y = homeowner policy…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Given the LP Model Minimize: z = x- y subject to: 4х — Зу s0 x + y < 10 х, у 2 0

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Q: 1 V5x + 4

A: We have  ∫1x dx=2x.

Q: Find for following 1.y = (x + v3x)S

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

Q: Let x~ exp (A) Show that T=s Xi is sufficiency Statistic.

A: Generally we use factorization theorem to obtain the sufficient statistic.

Q: The regression function r(x) = E(Y|X = x) minimizes E(E((Y − r(X))^2)). Is this true or false?

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Q: Evaluate the integral. S. sec Sx dx sec 8x tan 8x - In|sec Sx + tan Sx| + C 1 sec 8x tan 8x + In|sec…

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Q: Let X be gamma-distributed, with Var(X)= 2E(X) and moment generating function M, (3/8)= 2. %3D…

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Q: Let Ximexp (A). Show i Sulficieny that T-ZXi is Statistics

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Q: (2x+4) + 1 x² +2x- 10 dx = x² (x² + 4x +5) (2x +4) +1) dx- x² + 4x+5, Consider dx evaluate | x² + 4x…

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Q: 1 Find the most general antiderivative of the function x3 + 4x

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Q: Find an antiderivative of (3x3+9x5)/x6 in the variable x where x does not equal 0.

A: From the given problem:   3x3+9x5x6   So,    3x3+9x5x6=∫3x3+9x5x6dx   We can simply write as:…

Q: 4Vo Find the critical points of S(x) = x² +

A: Given Sx=x2+4V0x

Q: Find the total differential z = 5x3y2

A: The given function is z=5x3y2. Total differential: Let z=f(x,y) be continuous on an open set S. Let…

Q: Identify the transacation of point P x + 3, y + 1). ddf2d92a ddf892d342a ddf892d342a dd1892d342a…

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Q: Find the marginal PDFS fx (x) and fy(y).

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Q: S de x² –2 x+1 A x2 --x - In Ix + 11 + C C x2 +x - In Lx + 11 + C B x² -x + In Lx + 11 + C x2 +x +…

A: Given ∫x2-2x+1dx. The objective is to evaluate the integral.

Q: The ops y' =esx-7Y;s Separable

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Q: The coefficient of correlation between X and Y is - and o = a, of = 4a, and %3D %3D ož = 114 where Z…

A: Given: Z=3X-4Y. The coefficient of correlation between X and Y is 13and σx2=a, σy2=4a,σz2=114

Q: Evaluate the integral. 3x-7 (a) S- dx x2-2x-8

A: Answer and explanation is given below..

Q: 8. Find the orthogonal trajectories of y = cx CX

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Q: et Xi- Nco,1) and n=2 T=X,+Xz Show that Tis Sufficiencs y Statistic

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Q: Consider a risk process with X, ~~ y(2, 2) with loading factor 15%. Using the approximation eR* * 1+…

A: Solution

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

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Q: Evaluate the integral: dx 4 4V x -4 + =(x²-4)/2 + c 8 x - 4 + 3/2 + C ******** 3/2 (x²-4)2 + C -4+C

A: We have to evaluate the integral value.

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

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Q: What value of x minimizes C = 0.005x2 provided that C must be positive and x is within (0,1)

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Q: 39. Use Leibniz's Rule to find the value of x that maximizes the value of the integral px+3 1(5 – t)…

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Q: 3 Find absolute extrema for fCx) = x°-9x´+15x -3 %3D in terval [o,3] Oへ

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