4.2 Let Fj, be a closed set for k = 1,2, ... ,n in (S, d). Show that U Fk is closed.

Q: 18/156) If the Wronskian W of f and g is te' and if (t) = t, find g(t) %3D

A: Given that gx, y=t2et with ft=tTo find gt

Q: Let G = Z31, S = {1,5, 6, 25, 26, 30}. %3D %3D Prove that Cay(G, S') is normal.

A: It is given that

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

A: Given that  Let X  N(μ,1) of size n. Obtain UMVUE for μ

Q: 2 Let F be a closed set for k = 1, 2, ... , n in (S, d). Show that |J F, is closed. k=1

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

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: Let E = [-2, 3) U {−3, π}. Determine the following max D inf D interior of D boundary of D closure…

A: Solution:-

Q: 3;) Find the välie of k isó that. the furnictioin %3D .kx*. .if. x 2 2. is. continuous .cvery iw…

A:

Q: Find yas a fon chenof x if t. %3D with

A: This is cauchy euler equation and we will solve it by changing the dependent variable

Q: If S, T are nonempty bounded subsets of R with S ⊆ T, then inf T ≤ inf S ≤ sup S ≤ sup T.

A: Since S ⊆ T it follows taht inf T ≤ t, ∀ t ∈ T, then  inf T ≤s , ∀ s ∈S:Therefore inf T is  a lower…

Q: O Let X,X. X3 beasamPle of size n=3From the Bernolli Pmf Assune Ti ヒ(X、メ,メ) X、+メz+Xg and こ I= X,X t…

A: Using the Neymann factorisation theorem we can find out the sufficient statistic.

Q: Find the fowien senies fon | X), -T<X <A

A:

Q: Let (W, t > 0) be standard BM. Show that P(n|w,1 – Wa sc) → as n → 0.

A: From the given information,  (Wt, t≥0) be standard Brownian Motion. Note: In the given situation,…

Q: 3. Find all the fixed points and classify cach of them: f(r,u) ryev,

A: Solution:- Fx,y=xye-x2-y2 Put Fx=0 and Fy=0 Fx=e-x2-y2y-2x2=0and Fy=y-2y2 e-x2-y2=0 So,  0,0,12,12,…

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: 15. Given nonempty-subsets of R², say Y1,..., Yn, let Y* = {E÷=1 Y; | Y1 € Y1,.., Yn E Yn}. Given p…

A: Given: Y*=∑j=1nyj | y1∈Y1, y2∈Y2, ..., yn∈Yn and, for any p∈R2 and nonempty subset Y⊂R2, vp,…

Q: 4) Which of the following foumulas does not Kold for all x, we CZ O la wl= |2). Iw). (6) X W = ņ. W.…

A: We know that

Q: Exercise 2. Suppose V and W are finite-dimensional, T E L(V, W), and there exists PE W' such that…

A: Given V and W are finite dimensional , T∈LV,W and there exists φ∈W' such that nullT'=spanφ We have…

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: Qt Let T= {carb) a,b ER\fopp and of defined onI by Carb)*(c,d)= (ac, bd) for all (a,b), (c,d ET,…

A: The set T is defined as, T=a, b | a, b∈ℝ\ 0 The operation * is defined on T as follows, a, b*c,…

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

A: Given, And

Q: Show that R³ is spanned by S = {(1,1,1), (1, –1, 0), (0, 1, – 1)}.

A:

Q: Suppose that U(x; y) = xe' + ysin z, and that x, y and z can be measured with maximum possible…

A:

Q: Show that R³ is spanned by S = {(1,1,1), (1, – 1, 0), (0, 1, – 1)}.

A:

Q: 1. Let TE L(V) and suppose v is in the range of T and w is in the null space of T". Show explicitly…

A: To solve we will use the definition of adjoint operator.

Q: For G = S, state Question 11. necessary and sufficient conditions on T , a subset of S = {1, 2, . .…

A:

Q: PO しl Let 4Let R be the reaion enclosed by oe en closed by Jhe graphs [sreph R ont omt y=8; x= o ind…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: (X,) is a sequence of independent identically distributed positive RVs, where E(X,) = a and EX,'=b…

A:

Q: Let S be a nonempty bounded subset ofR. If for every e > 0, there exists an x E S such that x > b -…

A:

Q: 3. Show that X = (x|Ax=b, x ≥ 0} is convex. following ure which no

A: As per our guidelines we are supposed to answer only one question.

Q: 4. Let f : R" → R", x+ Ax + b be an affine function, where A E R"xn,beR". (a) Show that if X CR" is…

A: Let f: ℝn→ℝm be an affined map defined as x↦Ax+b, where A∈ℝm×n and b∈ℝm. Then it follows: fx=Ax+b…

Q: Let Á = ry?a, + x³yzay, Evaluate A. dl along the path y = x2 from a(0,0,2) to b(3,9,2) Select one: O…

A: We will find out the required value.

Q: [2.13] Let S be a nonempty set in R". Show that S is convex if and only if for each integer k > 2,…

A:

Q: 3. DETERMINE THE UOLUME OF THE REGION BOUN DED ABOUE BY THE PARABOLOID Z=2-x²-y BY THE CON E

A:

Q: 6. The distance between a point x ER and a nonempty set A CR is defined by d(x, A) = inf {\x – y| :…

A: In this question, we have to prove that d(x,A)=0 iff x belong in closer(A)

Q: A chow that the wsonskian d es will neves become zex0 to8 all spal

A: Here we use the fact ex&gt; 0 ,for all real x.

Q: 1- Suppose that ,p) is a meric space, an that E CX. Then the interior E is open (m X) and the…

A: The given question is related to metric spaces. The solution is explained below.

Q: In general, for a a) S is compact 2) Sis closed at S is compact

A: We use definition of compact metric space, totally bounded set, Closed set, accumulation point or…

Q: (X), E(Y ) EXY), Cov(X, Y) , σχ, σχ and Py.

A:

Q: of E. 4. Let E CR be a bounded set. Prove sup E e Ë.

A: (4) Let E be a bounded subset of R  and let u be the sup E.  Then two cases arise-  Either u belongs…

Q: Please solve this linear algebra question. Thank you.

A:

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

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

Q: Let SCR and let c e R be a cluster point of S. Prove that for each e >0 the set W := Sn(c-e,c+e) has…

A:

Q: Let fons =loag, Cln). Find t'ot at

A: Given, f(x)=logx(ln(x))

Q: 5. Let TE B(H). Show that (ker T)- = ran T.

A: Given: T∈BH and T† is an adjoint of an operator T. To show: ker T⊥=ranT†

Q: Show that R3 is spanned by S = {(1,1,1), (1, –1,0), (0, 1, – 1)}

A:

Q: 3. Eliminate B and a from the relation x = Bcos(wt + a) in which w is a parameter not to be…

A:

Q: 2. Write a preference E on R as a subset of R', where a bundle a E Rª is at least as good as a…

A: To write: A preference ⪰ on ℝ+2 as a subset of ℝ+4, where a bundle x∈ℝ+2 is at least as good as a…

Q: If e-ispure imaginary W hat Restriction is placed on z?

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.