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) n/chk)

Q: 10 of 17 If y(t)+(t-r)y(r)dr=t, then y(t)= Su-nyndr3Dt,

A: Convolution Theorem: The Laplace Transform of the convolution of f(t) and g(t) is:…

Q: A population consists of 4 units with values 156, 149, 164 and 155 respectively. Draw all possible…

A: Given that Population size N = 4 Sample size n = 2 Then possible samples WOR are NCn = 4C2 = 6

Q: Howin If Z=RCxy) and u=xayg V=x-y show that 3

A:

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: De Morgan's law

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Q: Find diagonal matriy D is similar with A a A = [3 8-5

A:

Q: 5. Show that if x,y∈Z and 3|x^2+y^2 then          3|x or 3|y 6. Show that if c=sa+tb where c=(a,b),…

A: Please check that x=1,y=3, then x^2+y^2=10 does not divide by 3. So  must 3|x and 3|y instead of 3|x…

Q: Grien V=In (xity?) show that dye

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Q: Compote clerivative bao fx)= cot(x), x=0.8 flx)=cot(x, %3D fl0.8) =

A: We use basic inverse trigonometric identity.

Q: Consider the Venn diagram below. Illustrate the other De Morgan's law by selecting the region(s)…

A: GivenAc ∪ Bc

Q: 18, then Ku = 3 and µ4 Af U2 %3D %3D Select one: O Platy O symmetric O Lepto O Meso

A: Solution-: Given: We find

Q: 4).ェ Pare subset, -f y such that CeD than fic) is not eD, then the Convers %3D そイue.

A: Solution As it's mention C=D and f^-1 same , so each and every element from  f inverse we get equal.…

Q: Let Z, = 2 cis 30° = 3elli %3D Z = In (1 + i) %3D If Z = Z,Z, + Z, Find Z].

A: From the given information. Write the complex numbers Z1, Z2 and Z3.

Q: 2)Evaluate exdA ,Ris bounded by y = x² ,y = 1

A: By using Fubini's theorem we solve the given problem.

Q: Let X ∼ Bin(n, p), and let Y = n − X. Show that Y ∼ Bin(n, 1 − p).

A: Here X follows Binomial with parameters n and p. Here, Y=n-X. Then Y takes the values n-0, n-1,…

Q: 3.5 30 21 Not drawn to scale. O SAS- Theorem O SA- Postulate O SSS- Theorem O AA- Theorem

A: There are 2 theorems for similiar triangles. SSS and AA theorem

Q: Suppose that (Q x Q, +,.) is a ficld where (x, y) + (z,w) (x+z,y + w) and (x, y). (z, w) (xz +2yw,…

A: I have find identity of the field and then inverse

Q: find the'mters ection d Exe sy,z]= [a,0,31++ 4,-2,178 [+sy,z]=[6,-12,--11]+5 [1,2,4]?

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Q: 16. Write a two column proof. Given: OSTUV U V. Prove: AVXS = AUXT T S 8.

A:

Q: Con sider Sam ple X,, X2,.., Xg from a NC8,4). Find the Coverage Probabilit a of interval [x-2, +2].

A:

Q: 8. Show that, for u, v E R³, ||u|| ||| = (u - v)² + ||u x v||².

A:

Q: (6) If u, =*-!P«(x)Pn -1(x) dx, show that nu, + (n – 1)n-1 = 2, %3D and hence evaluate u„.

A: Given un=∫-11x-1PnxPn-1xdx

Q: Let W = Lin and U= Lin 2 (a) Show that R' = W U. Explain.

A: Note:- As per our guidelines, we can answer the first part of this problem as all the parts are…

Q: H.wBy using C.R.C., ind the lerivative of hea)=121? if it exist.

A: Hello. Since your question has multiple parts, we will solve the first three parts for you. If you…

Q: If delta is large according to Cohen's classificantion, then the difference between u1 and u0 is…

A: Given that - If delta is large according to Cohen's classificantion, then the difference between u1…

Q: 3. Show that S, has the presentation (x, ylx* = y? (xy) %3D %3D

A: Given: Group S4 We need to show that S4 has representationx,y|x4=y2=xy3=1

Q: Let X and Y be independent and distributed as N(mu, 1). Is T=X-Y sufficient?

A: According to factorization theorem, if the likelihood function Lx,θ can be expressed in the form.…

Q: Find and when (TU – V)² In(W – UV) = In(2) at the point (T, U, V, W) = (1, 1, 2, 4).

A:

Q: Prove: For allintegers aandb, if a|b then a² |b²

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Q: B. If f = x²cosy + y²sinx then show that fry = fyx ух

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Q: (3) In R² with the standard topology: {(x, y) | x² + y² {(x, y) | x² + y? > 1}. = 1}, {(x, y) | x² +…

A: In a topological space R2with standard topology. A  subset O is open if at each point x in O there…

Q: In R4, let S = span{(1, 1, 1, 1)T ,(1, 2, 1, 3)T }. Find S⊥.

A:

Q: Find the maaimum and miniryem Valiaes of e feencteon Cif exits) feny) Luž-3ary

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Q: Let Y,, Y2, .., Y,~iid N (µ, o²) Find the MLES of µ,o? ....

A: Given Y1,Y2, ..., Yn~Nμ,σ2

Q: Ju 20²u c² of2 (r, t) = u(x,0) = 0, ut(x,0) = 0 u(0,t) = 0 u(1,t) = 0. da2(x, t) + XX , 00,

A: Introduction: The basic method to solve a partial differential equation is the method of separation…

Q: Compute ∮c (ydx+zdy+xdz) where C is the triangle with vertices (3,0,0), (0,0,2), and (0,6,0)…

A: The given points can be plotted as A(3,0,0) B(0,0,2) C(0,6,0)

Q: Prove that du Inlul + C where n= -1 u

A:

Q: 4. A region D in RN is said to be convex if and only if for every u, v E D and t e (0, 1), then tu +…

A: Given: A region D in ℝN is said to be convex if and only if for every u,v∈D and t∈0,1, tu+1-tv∈D.…

Q: Show the Complete S lu fwn i 3 ナ *

A:

Q: onsider two points (x0, y0) and (x1, y1). Prove that the first order Lan￾grange polynonial is…

A: There are two points (x0 , y0) and (x1 , y1) ,now prove that the linear Lagrange interpolating…

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

A:

Q: 7. Use Green's Theorem (and no other method) to show that the area of the triangle with vertices…

A: Greens theorem

Q: G be H and Ki Then direct 7(H) and Let direct pradeuct 7(G) Yoduct z'(k). is

A:

Q: (b) Using Venn Diagram to prove that (A U B)e = A° N B° ?

A: To prove the following using Venn diagram A∪Bc=Ac∩Bc First consider the left hand side  Set A

Q: c) Compute µr, Hy, Ož, o, Cov(X, Y), and p

A: Reviewing information, Given pdf is, f(x,y)=x+y                 ; 0≤x≤1 ,  0≤y≤1

Q: (a) Suppose ƒ: [a, b] → R is integrable and L(f, P) = U(ƒ, P) for some partition P of [a, b]. What…

A: (a) Given that f:a,b→ℝ is integrable and Lf,P=Uf,P for some partition P of [a, b]. To find: what f…

Q: Bla) 31 compute measurable

A:

Q: Pind using: 17 (a) Euler's Criterion (b) Gaur gn

A: We have given (517). we have to solve by using  a) Euler's criterion b) gauss lemma c) A primitive…

Q: Consider a S = {x|x"=1} is S, equals to S?

A:

Q: Show that a triangle with vertices (x,Y;), (x2,y2), and (x;,y;) has area + x,y3 + X3Y, – X,Y3 – X,Y,…

A: