Given: e || m Z3 = 24 1 Prove: e || n m 3 4

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.

Q: Let S, := (1 - (-1)"/n :n e N). Find inf S, and sup S,.

A:

Q: The largest interval for which the IVP : (In(e - e?)) y + y = 1, y(5) = 0 has a unique solution is O…

A: We have to find largest interval for unique solution

Q: 4. Suppose is a discrete rv with E(9X + 2) = 20 and E(X²) = 13. (a) Find E (X) (b) Find V (X)

A: a) We will use the formula E(aX+b)=aE(X)+b E(9X+2)=20E(9X)+E(2)=209E(X)+2=209E(X)=18E(X)=2   Answer:…

Q: 4. Write down the formula of the following rules for n = 12. (a) Trapezoidal Rule (b) Simpson’s 1/3…

A: n = number of sub interval let area of shaded region is given in the form of integral function i.e.…

Q: The solution of the IvP Elb+2)jl&+2)y=t", yL3)=o exists in the interval O 6, 00). noncof the giren…

A: given differential equation is t(t+2)y'+(t+2)y=t2,y(-3)=0

Q: 46. Let the assumed particular solution for the given DE be y, = (Ar³ + Bx² + Cx)e* + E. What is the…

A: A detailed solution is given below.

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: 0 <m < n such that am = e. (Hin

A: Subgroup generated by any element in a finite group will have at most n element where n is order of…

Q: Prove for all mEw and n E w, we have that m+ ·n=m・n+n.

A: Given that m,n∈ω. To prove: m+· n=m·n+n

Q: 0.6 e da, using Simpson's by taking EaN=6

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Q: Find the first term of: E (-1)n+1 (z+1)" n=1 3D1 O (z+1)^2]/2 Z+1 -(z+1) no solution

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Q: S - dz = In|e +5| +C %3D O True O False

A: we know that ∫f'(x)f(x)dx=log|f(x)|+chere f(x)=e3x+5        f'(x)=3extherefor…

Q: 25. Which of the following is the answer for secx = V2 A. E + 2nk|k E Z}U {+ 2rnk|k € Z} 3 B. G+…

A: We will solve the problem

Q: 1+ni Q1. Evaluate " e*dz along the path shown in figure below. n/2 1

A: We evaluate given integral along the path

Q: 2. Let P: C(0, 1]C(0, 1] be given by Pp "- e. Compute dP(x). Be sure to justify your calculations.

A: Given: The given function is  P:C20,1→0,1 given by pφ=φ''-eφ

Q: Which of the following is the general solution to (D-3) (D+1) y=0 Oy = (Ao+ At + A2t?) e + Be Oy =…

A: We have to find solutions

Q: solve the following P.D.E: azu ди + u at əx2 u(0, t) = u(1,t) = 0 (1, 0<x<1/2 10,1/2 < x <1 u(x, 0)…

A: Let the solution of the equation be ux,t=XxTt. On differentiating, we get uxx=X''xTt and ut=XxT't.…

Q: The largest interval for which the IVP : (In(e* – e²)) y' + y = 1, y(5) = 0 х —6 has a unique…

A: We need to find the largest interval for which the given IVP has the unique solution.

Q: (d) Are X1 and X2 independent? Justify. (e) Compute E(X1) and V(X1).

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Q: The largest interval for which the IVP: (In(e* – e)) y' + y = 1, y(5) = 0 %3D X-6 has a unique…

A:

Q: H.W: if w=√x2 + y2 + z2, x= erCose, yerSine, z=ee prove that aw/ar = e²r/w and aw/00 = e²0/w

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Q: m!n! If m, n e N, then prove that ,, dx = m.n (m+n+1)!

A: A detailed solution is given below.

Q: If e'z = /3 -i.Then Im (z) is %3D O a. e2 b. 0 С. 1 d. -In(2)

A: eiz=3-i Now let z=x+iy. Then, ⇒eix+iy=3-i⇒eix+i2y=3-i⇒eix-y=3-i…

Q: Given: RQ = TP ZQ = ZP Prove: RZ = TZ

A: Given: RQ=TP, ZQ=ZP According to given figure RQ=ZQ+RZ…

Q: eb Let A E M₁ (TR) be given If AAt = On HOME JATOT prove that A = On - Does this hold if A EMn (C)?

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Q: Show for R(t) = e?-t and S(x) = 2x + 1, that (Ro S)(x) = e1²+2#.

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Q: E Given: AC= BD D AE = DF ZA = ZD A Prove: ACAE= ABDF F

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Q: Show the following differontial quahion is hamegenous and Solve it: X*dy +C y-xy) dx

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Q: Prove for r ≠ 1 that ∑_(k=0)^(n-1)(rk)=(1-rn)/(1-r). If ∑_(k=0)^(n-1)(rk), then compute s(1−r) =…

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Q: ди пе 1. Given u = x2 + xy; x = r² + s²; y = 3r – 2s, find and ar - as

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Q: Suppose a E Z. Prove that for any n E N, 5|2"a implies 5|a.

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Q: QUESTION 5 Complete the proof using the drop-down menu. Prove: (A xB)N(C×D)c(ANC)x(B ND). VE(AXB)N(C…

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Q: Z1 is complementary to 2; 2 is complementary Given: 2 B 3 A E to 23 Prove: BD || AE

A: Prove that BD∥AE.

Q: - Given y= ela's -x²-In'r, what is y'?

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Q: 2. Let P:C0, 1] → C|0, 1] be given by Pp = " – e°. Compute dP(y). Be sure to justify your…

A: We have Pφ=φ''-eφ We need to find dPφ If we have  y=fx⇒dydx=f'x⇒dy=f'x dx Similarly, we find dPφ for…

Q: If m` E = 0, then E is measurable.

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Q: Is it worthwhile economically to purchase the annual towing insurance at a cost of $50.00? a. Yes,…

A: X = Amount spending on towing Probability Does not need to be towed $ 0 0.75 Needs…

Q: By applying the Convolution Theorem to calculate L-1{e n, with n E Z* , a suitable (s"(s- expression…

A: The given inverse Laplace transform is                                        L-11sn(s-5)…

Q: 19. Given: PR || VO; RO || PV; PR = RO Prove: 1 and 22 are complementary. R V. E.

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Q: For the following PMFS X and Y for k e {0,1,2,3, ..] Px (k) = { %3D otherwise for k e {0,1,2,3, ...}…

A: From the given information, PXk=e-λλkk!, k=0,1,2,3,....PYk=e-λλkk!, k=0,1,2,3,.... If λ=1, a) The…

Q: Q. By e/2silon definition, check the con vergenie of Suquenies 2n+ フ the following く Sn> = ( =…

A: Find the attachment

Q: et A E C. Show that |A| 1 if and only if A= e for some 0 E R. %3D

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Q: 03) find the ax en the sl abetwed wol y=J2-X, and y= 0

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Q: Find u(x, t) which solves the problem Utt = 9urr -00 < x < o0, - 0 <t <3; 1 u(x, 0) = 1+ x2 Ut(x, 0)…

A: D'Alembert Solution;    u(x,t)=ux,t=12f(x+ct)+f(x-ct)+12c∫x-ctx+ctg(ξ)dξ where u(x,0)=f(x),…

Q: he joint pmf of X and Y is given below. What is E()XI-M)? Y -1 1 X 1/16 1/16 1/16 1/8 1/16 1/8 1/8…

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Q: 4. Write down the formula of the following rules for n = 12. %3D (a) Trapezoidal Rule (b) Simpson's…

A: Solution:

Q: then Res(f(z), -1) is ez 1.5 Given f(z) = +1)' А. е, B. C. * _1 D. 0, E. None of the above.

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Q: Prove that e“ p.w. on R. n! n=0 M8

A: