. For j = 1,..., N, let Ij = [aj, b;] with a; < bj, and let I:= I1 x -… ·x In. Determine a1. (Hint: Draw a sketch for N = 2 or N = 3.)

Q: Complete the following proof. Given: FG FJ, HG = IJ Prove: HF = IF

A: I have provided solution in step2.

Q: Let {X;} be i.i.d.~ Exp(0) and a; > 0. Denote by Z = min{a,X1,..., amX,}. Suppose that 0. Prove that…

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Q: Prove that ||A||1 = maxi<j<n{E#1 laij|}. i=1

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Q: Given: LM NO; ZLMO = ZNOM Prove: LO NM ments Reasons

A: We have to Prove that LO congruent NM

Q: Tami Far oybe R for c>0 2)-lal s a Ś lal 3) ta +bl staI T In Proof: ) ) het lalsc ASC

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Given that en 2= V and en 3=W,express each of the fallowing in terms of vand w a) in zv0/3

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

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Q: Solve the following differenital equehims -1 2(-0 +g(t)), with (to) = e, ? dt

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

A: The solution is given as

Q: Suppose that > ak = a and let c E R. Prove, in all the that (c-an) = gory detail necessary, = c•Q.…

A: We will give two proofs one based on partial sums and the other will be a direct proof.

Q: Prove that tr(aA + bB) = atr(A) + b tr(B) for any A, B belongs to Mn× n(F).

A: We need to prove that tr(a A + b B) = a tr(A) + b tr(B) for any A, B belongs to Mn×n(F).

Q: Let X1, X2, be a nequence of ... independent and identically distubuted rvs, each having frñite mean…

A: The Chebyshev's Inequality:                    Let X be a random variable. If X has finite mean μ,…

Q: Let X - N(H, o). Show that the MGF of X is etu+to²

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Q: メ (myst メート→ Q(2,4) where: Path C くz rom ○)と to over the Evaluate the

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Q: Prove this! P (an) = W/ NM) [M-N (p-q)" ] 8 Npq %3D exp

A: your question is not clear i think some error in the question plz confirm it.....

Q: Given: 2OTS = LOES, ZEOS = ZOST Prove: TO = ES E s.

A: In △OTS and △OES∠OTS=∠OES                   (given)∠OST=∠EOS                   (given)OS=OS…

Q: 1. Prove with the usual notations that: (a) EV = VE = A (b) A +V =- (c) A= SE Apply the suitable…

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

Q: 3) Use the Second Principle of Finite I nduction to establish that for all nz I o"-1= (a-1) Co to ta…

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Q: Let c E R and suppose that an → a. Show that can → ca.

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Q: Let P = {p:p=6x-1, for some x EZ} and Q= {q:6y+5, for some y EZ). Prove that P= Q

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Q: 10. Let X , j= 1,.., n, be i.i.d. r.v.'s such that E(X,)= µ, o'(X)=o', both finite. j' Show that E(X…

A: The normal distribution: A continuous random variable X is said to follow normal distribution if the…

Q: o provethat WE =c? bWex W=tan (x-et) 3 prove hat f xx + Pyy = o whene fetan () 2.

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Q: Let Q be an m xn nauix with ni >n and orthanormal columms, then we have both Q' Q = 1, and QQT -1 O…

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

Q: Consider the following figure and proof. Given: RM || SN, RM 1 MS, SN 1 NT, Prove: ARSM-ASTN

A: Given: RM∥SNRM⊥MSSN⊥NT The objective is to prove

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: Given that A det(A) with det (A) + 0, consider the following statements: -67 d () aet( A) detaj…

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Q: Show that for every e>0 ther e exists P suuch that U (P, f) < U (f) + e

A: We will ise definition of U(f) and Infimum.

Q: Consider the figures below. N Which of the following statements are true, given S 4J and ZN LE?…

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Q: Let X ∼ Geom(p), let n be a non-negative integer, and let Y ∼ Bin(n, p). Show that P(X = n) =…

A: From the given information, Consider, X,Y are to be two random variable where x follows geometric…

Q: ), P{|Zn – c| > ɛ} → 0 as n → o. Show that for any b on g, E[g(Z„)] → g(c) as n→o

A: *Answer:

Q: (a, o) is not measurable. ylgn ihi

A: Given :-(a, ∞) is not measurable.

Q: Which of the following can you not use to prove A CAT S A DOG? 1. CA DO II. ZC ZD III. ZA E ZOo IV.…

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Q: Let a = 8 and b = 9. Find m,n E Z such that am+bn =1.

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Q: 30 Let A, B E M, and suppose that A² = 0 = B². Show that A and B are unitarily similar if and only…

A: I

Q: let it be T=11,2,3 } S:la,b,c] Proved P(TNS)E P(S)NP(T)

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Q: Show that for any positive integers i and j with i > j, we have T;(x)T;(x) = [Ti+;(x) +T;-j(x)].

A: we have to show, for any positive integers i and j with i&gt;j TixTjx=12Ti+jx+Ti-jx Now, we know…

Q: Use Shapiro-Wilks and a = 0.05 for the test and show all parts. * %3D Но: (а) На: (b) F and PValue…

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Q: (1) In the following sketch, prove that Â, +Ĉ, = B.

A: Given: The figure To prove: A^1+C^1=B^.

Q: Show that (t As) can be derived from the premises pq, q→~r,r, pV (t As).

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Q: Compute the length of the curve r(t) = (21, In(?), r²) over the interval 1 < t < 7. (Use symbolic…

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Q: let X~~ Per(P) Prove ô is unbiare if ô-X let x exp(0) Prave e is unbiar

A: Introduction: One random variable follows Bernoulli with parameter p and other random variable…

Q: O let T:R?→R² be a lineas tanafor- mation Such that T([:])- [ ]. T %3D Find matnie A Such that T(x)=…

A: Given that T:ℝ2→ℝ2 such thatT11=41  and T01=32 We have to find the matrix A such that Tx=Ax   ,…

Q: b. Let x, y,p E Z, where p is prime. Prove that x2 - p²y - p + 0. (Hint: you may use without proof…

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Q: (c) If A E M,(R) is non singular and n 2 2, prove that det(adjA) = (det A)"- (d) If A E M,(R)…

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Q: ke an example at a Noe therian m adu le is not Artini an.( Prove)

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Q: For any x E R, there exists n EN such that x < n; ylgn ihi

A: We have to state whether given statement is true or false.

Q: Let x, y,p E Z, where p is prime. Prove that x2 – p²y – p + 0. (Hint: you may use without proof that…

A: Solution :-

Q: Find the inverse Z-transtorm of he follows housing de X(Z)= tanh (z

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Q: The requved values tor a qud b tor Ple funston to be contimues at x=

A: Use simple continuity theorem.

Q: Let P= (p:p=6x-1, for some x EZ) and Q = {q:q=6y+5, for some y EZ}. Prove that P=Q

A: