5. If A e U(n) and A e C has length one, show that XA € U(n) .

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: if Z= とan'Y final dž In Point C!,!)

A:

Q: 69. Let F(x, y) = (x,0). Prove that if C is any path from (a, b) to (c, d), then F. dr (o2

A: Given: F(x, y) = <x, 0>. C is any path from (a, b) to (c, d).

Q: Suppose that X, Y C U. If Pr(X) = 0.3, Pr(Y) = 0.32, and Pr(X n Y) = 0.08, what is Pr(X' U Y)?

A: Given :  X , Y ⊆ U . P (X) = 0.3 , P (Y) = 0.32  and P(X∩Y) = 0.08 .  To find : P (X' ∪ Y) = ?   The…

Q: Let X N (u,1) of size n. Obtain UMVUE for M.

A: We will use Lehmann-Scheffe theorem to find the uniformly minimum variance unbiased estimator for μ.

Q: 8. Given that r || s and transversal t, 21 and 26 are supplementary.

A:

Q: 12 3. If u lx + my, v = mx-ly, show that ди 4 + m

A:

Q: If u (E) =0, then E is measurable.

A:

Q: If the rst line has the form Ax + By + C = 0 and the second line has the form Dx + Ey + F = 0 and…

A: Given,  The first line  Ax + By + C = 0  and  is to pass through the origin  The second line  Dx +…

Q: 10, elseunére Y,= amonnt ok pollutant Per Sample collected a bove the Stack WHhout the cleaning devC…

A:

Q: Find and plot the cubic spline S satisfying S(0) = 1, S(1) = 3, S(2) = 3, S(3) = 4, S(4) = 2 and…

A: %File Name: findSplineCoefficient.m %Define function function [ retCoeff ] =…

Q: Construct the fundamertal soluton G(x, E) -?G= S(x- E) X, E ER? with, as x -E00 or

A:

Q: 25 If A E M, is symmetric, prove that AT is symmetric.

A: Symmetric matrix

Q: Prove that on average, permutations of length n have H, cycles, where Hn i=1

A:

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

A:

Q: In SRSWOR show that E(y )= Y

A: ANSWER: For the given data,

Q: Suppose RV X has the following PMF: p(0)=0.2, p(1)=0.5, p(2)=0.3. Find E[X], E[X^2], E[X]^2.

A:

Q: Find the length of the curve y = In(e - 1) – In(e + 1), In 2 sxsIn 3.

A:

Q: If E, and E2 are measurable then (E,UE,) is not measurable .

A:

Q: and Z , if y=0 Solue %3D By using Direct melh oel.

A:

Q: . Show that z)= E kz is D: 1215 continuous io domain

A: The series can be shown as continuous in a domain if it converges. Therefore, the first calculate…

Q: 3 - find " if w z 4 e Lny and X = hn(ucosul y = = Usinv = usinu , cu v) = (2,) cugv) = (2,

A:

Q: locally Lipschitz in (t,x)E[a, b]x D.

A:

Q: The Wronskian of y,(t)=e 2, y,()=e" is-e St. Select one: True False

A:

Q: 4 Let X,) be a pankizlly oadered e For x,y € X deftre xLy eff x sy and x#y. Pucose the Fallowiag:…

A:

Q: 4. In AMAP and ATIE, LA = LI and ZP = LE. a. What is the relationship between ZM and ZT? b. If mZA=…

A: Given:- In ⧍MAP and ⧍TIE,∠A = ∠I and ∠P = ∠E. To find:- a. What is the relationship between ∠M and…

Q: 4. If E(R) exists, show that |E(R)| < E(|R]).

A:

Q: -2 -In x SLy e dz dx dy O 7/24 O 7/48 O 5/48 O 47/24

A: We have to find the integral.

Q: Σ (X) E(Y), E(XY ) , Coν ( X, Y) , σχ, σχ and ρxΥ.

A: As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted...…

Q: Suppose, X0- Binom(m,0)and 0~ Beta(a, B), then E(X) is equals to, a) maß b) aß ma c) d) me

A: Given: Suppose,  Xθ~Binom(m,θ) and θ~Beta(α,β)

Q: I, Fund warginal X warginal h(x) alistribution for 2. Fud conditimal pf Ty) Estmate 4. Estuale…

A:

Q: Determine if the following is a fundemental set of solutions to  y'' -6y' + 25 = 0 Given that…

A: If the Wronskian of two solutions is not equal to zero, then the given set of solution is…

Q: (10) If H < Z» × S, with |H| = 12, then H = %3D

A:

Q: 1. Prove that given a line € and a point P not on e, there exists a line through P perpendicular to…

A: Explanation of the answer is as follows

Q: Show that E(SSE) = (n - k-1), as in Theorem 7.3f, using the following approach. Show that SSE = y'y…

A: Please find the explanation below. Thank you

Q: (6) If w = f(u, v), where u = x + y and v = x – y, show that = 2 ди

A:

Q: 28. (a) Prove that for x e R" and s < t, Ds(x) C D;(x).

A: The notation Dsx represent  an open ball of radius s, centered at x∈ℝn. Let x=x1, x2, …, xn,…

Q: 1. Let P, X,Q denote distinct points of E. If X is between Pand Q, show that d(P,X) d(X,Q) 1-t, for…

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

Q: If y= In Cschx + coth y Biod dy

A: Given: y=lncschx+cothx

Q: 1. If x, y, z E R, prove that (a) \x+y\ < \x| + \yl- (b) |x– y| < |x – z|+|z– y|, and (c) ||지| -…

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

Q: If g(a) = a°(exin²a+eoa²a), then gʻ(a) is: atcos.

A:

Q: B/let Flx)=[X]-X,x E(-2,2).which valuesof x o E(X) continuaus?

A:

Q: t, for t > 0, sa X 2 is

A:

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.…

A:

Q: 1. Let x (x,) E l. Find x if 11-- a. x = 2 %3D

A: This is a question of functional analysis in lp space.

Q: 7. (1)ydy - (y+)e de diferansiyel denkleminin genel çözümü aşagıdakilerden hangisidir? 4090 o e…

A: 7. Given differential equation is ex+1y dy=(y+1)ex dx. We will solve the differential equation by…

Q: 7) If z(x,y) = x² + y², x=u+v, and y=u-v, find dz du

A:

Q: Suppose / (s) - (÷)*" valuate: Js(x) dr +C 3- In (5)

A: Given      f(x) = 1512-3x

Q: e){x*,x%,x}on(0,)

A: