1. Prove That E (ri + si) a; = E}-1ri a; + £?=1 Sį a¿ 2. Find E(-1)k+1 (2k) k=1 3. Given X = 2, 4, 3, 7, 6, 3 Y = 2, 7, 3, 3, 1, 4 Evaluate (E*) Xị i=1 %3D1 2.

Q: 12. Define def M e-$dWg• s=0 For each t > 0, compute (a) E[M¡]. (b) E[M?]

A: Given  Mt=∫s=0te-s dWs      , where W is a Brownian motion.

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A: Given: 25-2 design is given.The results…

Q: A 2³-2 design was used to investigate the effect of A = condensation temperature, B = amount of…

A: Since, you posted multiple questions, we will solve 3rd question for you.

Q: Observations on the yicld of a chemical reaction taken at various temperatures were recorded as…

A: Given information: Given the yield of a chemical reaction taken at various temperatures as x(C0)…

Q: a=t). CTaylon Serie) 2-X Ln +x) (MacLurinSeries

A: We need to find the Taylor series of f(x)=12-x at a=1. Taylor series of function fx at a is defined…

Q: 21 Sımplify khe Following 221E36)+5-Ei0 -36+5+10 -36+15 -21, 222. V2*+i|

A: Objective is to simplify.

Q: 3. r= 2(1+ cos()) kardiyoidinin içinde r = cos(4) çemberinin dışında kalan bölgenin alanı…

A: We solve this by using double integration.

Q: Let n e N, s > 0, a > 1. Show that n! 1"e" dr sn+1 Inz dr 1 (a – 1)2

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Q: If z' + In(e el + e²) = 0 dz find ar at the point (0, 0) O 3 0 -3 O 2 O-2 « Previous

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Q: If a chemical bond vibrates at a frequency w, the average energy of the bond turns out to be equal…

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Q: 1. Compute E(1/X) 2. Find the cdf and the pdf of Y = 1/X 3. Compute E(Y) and compare this result…

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Q: 8. Given that (2x-x*); 0<x<2, S(x) = ; elsewhere. a) Calculate E(X), E(X²) and E 2- X

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Q: Given that a 50.0 kg test run of gas averages 10.0% H2, 40.0% CH4, 30.0% CO, and 20.0% CO2 m mass,…

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Q: l'Hôpital's Rule

A: Given equation

Q: 1. re (x, y, z) x). Ly). (z}} - *(*. y, z) . (x)S(x), ly), (z]} (x)E (x, y, z}

A: If x is element then it belong to set And {x} it will be subset of set

Q: 1. Assume beta*(1+i)=1. y1=100 y2=20. beta=0.8. c1=______ c 2=______   2.  Assume…

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Q: Prove the following: (a) E (C X) = Č E(X) (b) E (X + Y) = E(X) + E(Y) (c) E (XY) = E(X) · E(Y) When…

A: Answer: For the given data,

Q: e a. y; = +e-2= In(e" +1) +e-* In(e" + 1) – 6 2 b. Y, = re2" + e In(1 + e") – e2" In(1+ e") C. Y; =…

A: Option (a) is correct.   See the solution in the attachment.

Q: 2 Calculate e(0) and e(0) for 1.98z E(z) = (z? – 0.9z + 0.9)(z - 0.1)

A: Ez=1.98 zz2-0.9z+0.9z-0.1Now put the value z=0E0=1.9×00-0+0.90-0.1=0Becouse 0x,x≠0⇒0Now E(z)=1.98…

Q: If z + In(e3* - e + e²) = 0 dz find at the point (0, 0) -3 -2 3. 2.

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Q: 20. In(e**) = e2iny A. = - D. = dy В. dx dy dy С. dx dx у dx

A: Given equation is ln(ex^(2))=e2lny

Q: Consider the model y, , + e, where for X= {r1,…..,¤N}, and for all i, E (e|X) = c # 0. and Var (eX)…

A: From the given information, yi=γxi+ei X=x1, x2, ...., XN Eei|X=c≠0 Varei|X=σ2 Here, the ols…

Q: 2. If g(x, y) — In(ху + у — 1), find (а) g(1, 1) (b) g(e, 1) (с) g(x, 1) (е) д(х, у + k) (d) g(x +…

A: The solution of the problem is given in the next step.

Q: 1) Evalúe a) csch (In 3) b) cosh (0)

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Q: 1 1 et A = Verify the following 1 4 equalities are true or false, by computing each erm. If A E Mmn…

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Q: - S e-ttat1-1 dt a # 1 a '0

A: We use the definition of the Gamma Function to solve the given question.

Q: If 8(x) = [e²-m (21+ - dx S[e²-In (21+1) ]dt, find g(x). -2 A e-In(2x+1) 4 B (2x + 1)² 2 Ⓒ (2x + 1)²…

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Q: alpha iõtä 100 rhô 2 beta 20 kappa 200 sigma K 3 gamma 30 lambda 300 tau 4 delta 40 mu 400 upsilon 5…

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Q: A) B) A P E в ATSB = A by ABDA = A by.

A: A). In

Q: (9) The coefficient of correlation between X and Y is and of = a, oỷ = 4a, and %3D o; = 114 where Z…

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Q: M N * LN = MO SS SAS AAS AONL E AONM ALON E AMON ALNO S AMON

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Q: et X Xn XB(I,0) since X isthe mike for e then X(1-X)is the mil-e

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Q: 2.4.10 Show that det(e4) = etr(A) for all A E Mn(C). D %3D

A: The given problem is to show the given identity. To show: det(eA)=etr(A) for all A belongs to Mn(C).

Q: 21. |'t cosh t dt Jo

A: Note:- These are multiple question and according to our company guideline we can do maximum one…

Q: 1. Given that X1 = 1 X4 =-2 Xs = 4 X6 =-1 X7 = 5 X2 = 3 X3 =0 Xg = 2 X9 = 10 %3D Γind (a) E X;, (b)…

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

Q: Let Xi. ---- Xnd Glle e) and Tet TX = Exi , a) show tha T) is unbiased estimator for WcO) =nG: E…

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Q: Sheet 4 Numerical analysis dx QI/ Evaluate Jo 1+x2 Simpson's 1/3 rule Simpson's 3/8 rule i- ii-

A: In the question we have to find value of integrals.

Q: QUESTION 5 Given that the average value of (x) = 8.1x 5.4ax+ b on the interval [0, ] equals 23, then…

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Q: 47. Let the assumed particular solution for the given DE be yp = (Ar + Bx² + Cx)e + E. What is the…

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Q: 4 In(t) dt

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Q: 9. 3cos(@t – a), where w and a are constants.

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Q: 4 Ruret MC w co , , d, 7 the y a Fid e co f de

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Q: If z3 + In(e 2 -2 e+e) = 0 az find at the point (0,0) O -3 0 3 О-2 O 2

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Q: The Beer-Lambert law relates the absorbance A of a solution to the concentration C of a species in…

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Q: %3D in Fin d E(S an d Var(s)

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Q: Differentiate the function

A: Recall the following facts on differentiation.

Q: асe of A is

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.