Prove that Ks.s has (s-1)!s! s S13! . Hamiltonian walks for s > 1. 2

Q: Let {y;: t = 1, 2, ...} follow a random walk, as in (11.20), with yo = 0. Show that Corr(y, y;+h) =…

A: It is known that if yt follows random walk, then it can be written as yt = yt – 1 + et, forl all t =…

Q: let f: [o,0o] - [o,00) be decined by Fla) =x? IF is a homeomor phism Detemine

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Q: following table: x 1 2 4 5 7 8 1 1 2 4 5 7 8 2 2 4 8 1 5

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Q: 1nnd the x-iner and yitro tn caumon. Then gopn we conon uing grapining poper snon Oution

A: Note: We'll answer the first question. Since the exact one hasn't specified. Please re-submit the…

Q: For two R-modules Mand N Show that Hom (M,N) any with the composition is not agroup?

A: Given that M and N are two R-modules. We have to show that HomM,N is not a group under composition.…

Q: 5. Prove that S(n +1, k+1) = £ $(m, k) (").

A: To prove- Sn+1,k+1=∑m=knS(m,k)nm The falling factorial is defined as the polynomial,…

Q: 6. Show that the sets S = (1,5) and T = (0, 00) are equinumerous by finding a bijection from S to T.…

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Q: Let n, k, m EN with n2k21. prove that

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Q: Hor what salue of e dois th. a tollowng matrex haue an Tnverse Q. 2. 2.

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Q: Compute the orthaganal piojectian of ? onto the lina L through -6 and the origin

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Q: ands 1. Let m*(A) = 0. Prove that for every B, m" (BUA) = m" (B). %3D %3D

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

Q: If sup(S) exists, then it is unique ylgn ihi

A: The solution is given as

Q: Graph the limaçon. Limaçons with an inner loop r = 1/2 + cos u

A: To graph r=12+cosu

Q: (4b) Is Tâ onto? How do we know?

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Q: 15) o veclovs ú = Givetw and Tñ=211 deternine the projection d on 2.

A: This question can be solved using the projection formula.

Q: (3) OSJ A traffic Control engineer reports that 75% of the Vehicles Passing through a check Point…

A: As per guidelines expert have to answer first q question only.

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

A: False.

Q: Suppose A-( ) and One of it's eigvalues find ayae s js bhen alaef

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

Q: Solve the loieal Vahue Pr blem by the characteristic Hethod Using For a) flx)> 1 and A fx)- K.

A: Solve intial value problem Solving by characteristics equation

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

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Q: 11. Let S= {| -2 }. Show that u= E span S. 1 2

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Q: Show that if A is nonsingular and AB = O for an n × nmatrix B , then B = O .

A: We have given  matrix A is non singular and AB=0 for an n×n matrix  B. We have to prove that B=O

Q: 14) Find the Jacobian of the tra nsformation. x=5u-v,y=Du+3v

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Q: Prove that if n 2 3, the only element o of S, satisfying oy =ya for all y E S, is the identity…

A: Let n≥3. Let σ∈Sn such that σγ=γσ for all γ∈Sn. Suppose σ≠i, the identity Then there exists…

Q: Suppose T: R + P, has an action on a

A: Given, And

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

A: Here we have given E1 and E2 are measurable sets

Q: 2. If N = 14, k = 5, and n = 6. Find P(3). %3D %3D

A: Given: N=14 k=5 n=6

Q: 8. Suppose E is a nonempty subset of R. Show E = aEUint(E) %3D

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Q: Give three examples of Bernoulli rv's (other than those in the text). (Select all that apply.) Ox =…

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Q: is poisson (n)o Xn = Zn-n let En is. %3D 1. Normad cor) by himihing Runchien Moment-Gene rating…

A: Given  Zn~ POIs(n)  We want to prove that Y is the distribution of standard normal distribution

Q: PJ Prove that the trape z0: dal formula is go are a Az Ih( bit be) 2 bz

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Q: Find an explicit formula for s, if so = 1 and %3D Sn =2+2s0 + 2s1 +... +2s, 2+ Sn-1, Vn >1.

A: Generating Functions for a sequence a0, a1,a2,………an,……………… is an infinite series of the form ,…

Q: For all s, Isin s≤ 1

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Q: Prove that a complete bipartile graph Ks,s has (s−1)!s!/2 Hamiltonian walks for s >1

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Q: let z- 5 dy By chain Ruie

A: Given z = √x dy/dx = (1/2√x)•(dy/dz) We have to find d2y/dx2 .

Q: Which of the following statements is/are true? i. The vertices of K4 all have degrees equal to 3.…

A: In the complete graph ( Kn) with n vertices , each vertex is connected to the remaining n-1 vertices…

Q: Prove the following idenlity A-V = VA

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Q: Given: mAB = x Prove: mz1 = 180° - x A D Exercises 25, 26

A: Given:           m AB⏜ = x   To prove:              m<1 = 1800 - x

Q: Prove Bernoullis n=2,3.e incguality (ite)^Itnx or

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Q: @ 2 show Hhat fox) = e*-x3+2 2+2 is a %3D Permutation on R.

A: In the give question we have to show that the function f(x)=e-x-x3+2 is a permutation on ℝ.…

Q: 5. Which of the following statement(s) is/are TRUE about the Jacobi and Gauss-Seidel methods ?

A: For the given methods, statements II and IV hold true.

Q: 2) Let mf lu and (a,m)=| a,bE Z such that Let h= Om ( a) show and and (h,m)=1, %3D let. ne OmCab)…

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Q: Calculate and for the n = 2 state of a particle in a one-dimensional box of length a. Show that:…

A: As per the question we have to find the expected value of the position <x> and the expected…

Q: Let fELoi Show that i for any E>o, the set 3- S has a positive measure -

A: For f∈L∞ , f∞=infM>0:μx:fx>M=0For M>0, defining the set AfM=X:1 fx>M⇒For f∈L∞,…

Q: Show that if E,=1 a, diverges, then En=1 | |a,| diverges. %3D

A: Given, We want to prove that

Q: Assume C and D are chosen at random from {1,2...,n}. Let pn be the probability that C + D is a…

A: The number of pairs (c,d)  with sum m2 is m2-1 for m2≤n and 2n-m2+1 for n<m2<2n. Hence,…

Q: 『/ f メ,メ K、 be ars fo U()e) Tet Yu be the Larsest s the n bservotien an unbiesed estometor fr 6? E-…

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Q: All of the following assumptions are true about homoscedasticity except that it Select one: O a.…

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

Q: A prove that Newboń's for ward formal?

A: Note: Since you are asking the prove for Newton's forward interpolation, but the given formula is…