i. Given that : U= {x|x € Z, 0< x< 13}, A = {2, 3, 4, 5} B= {4, 5, 6, 7} C = {6, 7, 8, 9} D= {3, 8, 9, 10, 11}, find: a. CnB= b. U- (B UD) = c. ĀUĒ = d. B OD=

Q: Suppose, X|0~ Binom(m,0)and 0~ Beta( a,B), then E(X) is equals to, а) тав b) aß ma c) a+ B me d)

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

Q: (c) Infer E[W] without resorting to lengthy calculations but make sure you justify your inference.…

A:

Q: Given the three uniform dishribubions Dw and unknoun -where fur XNUE=8,0] wc havey=KlaULe,D]. Let XX…

A: a) Method of moment estimator for theta: let x1,x2,...,xn be the random samples from U[0,θ]. First…

Q: b) Consider the following simple AR (1) model Y: = u + Ø1ye + u, Show that the unconditional mean of…

A: # Given: AR(1) model  yt=mu+@1 yt+ut  where ut is white noise then to find unconditional mean of yt

Q: Let X - N(H, o?). Show that the MGF of X is etu+o²

A:

Q: 16) Use the given diagram to calculate P[(A U B)| C) A. 0.2500 B. 0.4127 C. 0.0848 0,25 0.02 0.01…

A:

Q: Given u(x, t) =t=?e, compute: e 2t

A: We have to calculate uxx of the given function.

Q: if w= fcu) and メ show that U ニ メャy? X Jw うx ニ0

A: We have given;

Q: et z = r²y – ry², I = e *,y= e*, then which of the following is O a. 2et + 2e 2t O b. 0 OG -2e4 – 2e…

A:

Q: part 4 of this problem

A: Introduction: Suppose A1, A2, …, An are n events, and A1ꞌ, A2ꞌ, …, Anꞌ are their respective…

Q: 10, elseunére Y= amount ok pollutant Per Sample callected a buve the Stack Wthout the cleaning devie…

A: Given  fy1,y2=1   , 0≤y1≤2 , 0≤y2≤1 , 2y2≤y10   ,  elsewhere

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

A:

Q: Given u(x, t) = t-²e¯, 2 , compute:

A: We can find the required answer as below.

Q: If R=10x3y2z2 and errors in x, y, z are 0.03, 0.01 and 0.02 respectively at x = 3, y = 1, z = 2.…

A: Consider the given formula as R=10x3y2z2. Then, we have…

Q: Show that, for all positive values of x and y, etty > e? ху

A:

Q: If u = cot ди then x x- y

A:

Q: If p (E1) = 0.3, p (E2) = 0.4 p(E1/E2)=0.5 so p(E1 cross E2)= 0.2 0.15 0.12 0.7

A: The conditional probability PE1/E2=PE1×E2PE2 substitute the values…

Q: ate f(c(t)) and ds = ||c'(t)|| i te Sc ƒ(x,y, z) ds.

A: Introduction: A line integral is a type of integral in calculus in which the function to be…

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

A: According to factorization theorem, If the likelihood function L(x,θ) can be expressed in the form…

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: c ls tE line cregmentfoom (3,4,0) to | (1,4,2) computef (zty?)ds&dp

A: The curve C is the line segment from 3,4,0 to 1,4,2. The parametric equation of this curve is given…

Q: After that, X independent fair coins are tossed and the number of heads obtained is denoted by Y.…

A: A fair die is tossed and its outcome is denoted by X,   X~116 216 316 416 516 616.   For k = 1, . .…

Q: Ho: 2.72 children H1: 2.72 children Calculate the test statistio, to

A: First we need to compute the Mean and Standard deviation of the grouped data provided to us : X…

Q: Let D={(x,y,2) : x2+y2+z?s 1600, z2 o}. Evaluate - z dv.

A:

Q: y' + y = y²

A: Given: Now,           y' +y=y2⇒dyy2-y=dtIntegrating both sides we get,⇒y=11-et+c1

Q: 2. Given s(x) = (1- ,0 <x< 100, 100 Calculate p(36) and E[T(36)].

A: Given information: s(x)=1-x100, 0≤x≤100

Q: and for the following situation Determine forulas for w=(z,y, ) 2=z (t), y=y(w, v, p), z==(v,p),…

A:

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

A:

Q: Let S be a randor mpute E(S|Z).

A: Here S be a random variable with P(S&gt;t)=e-t where t&gt;0 let Z=min(s,t) hence P(S&lt;t)=1-e-t…

Q: if T(x,y) = (x,0) then Null(T) = span{(0,1)} Select one: True False

A:

Q: 3. fualende Zdv, where, E- (nyE):0くn<l,o<y<1-n,oくまく1-1-

A: We have to evaluate the triple integral ∭E z dV where E is the region containing the set of points…

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: p(x, y) 3/24 2/24 1/24 1 2/24 5/24 2/24 2 6/24 1/24 2/24 Е(X), Е(Y), H(X), н(Y, НХ Ү), аnd HIX, Y)

A: It is an important part of statistics. It is widely used. Since the question has multiple sub parts…

Q: •1 Evaluate ſ, S, Saya xyzdzdydx S So Sirzava xyzdzdydx 2 0. Vx²+y²

A: 2) Evaluate ∫01∫01∫x2+y22xyzdzdydx

Q: et f(x, у, z) %3 ху + z', Р %3D (3, 9, 1

A:

Q: Let X, Y, Z C U. If Pr(X) 0.19, Pr(Y) 0.33, Pr(Z) 0.45, Pr(Xn Y) 0.07, Pr(Xn Z) Pr(Y n Z) 0.16, and…

A: Given DataP(X) = 0.19P(Y) = 0.33P(Z) = 0.45

Q: If W= R Cx, y,Z),g (x,y)=a,hcx,Z)= C, then Find dlw

A: Use chain rule of differentiation to solve this problem.

Q: Given R = Z₁₂, M = {0, 4,8], then R/M is

A: We know the definition of quotient ring ,  R/M = a + M / a ∈ R We have given that , R = ℤ12  and  M…

Q: Given that A = ax + Q ay + az and B = Q ax + ay + az, if A and B are normal to each other, Q is -2 O…

A: Orthogonal, or normal vectors have dot product equal to 0.

Q: Suppose that X, Y C U. If Pr(X) = 0.4, Pr(Y) = 0.22, and Pr(XnY) = 0.07, what is Pr(X' U Y)? %3D

A:

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-…

A:

Q: Let X, X2,..,Xg i.i.d B(1,p), where p = p(x;= 1) E (0, 1) the UMP test for Họ: P=0.5 VS H: P > 0.5…

A: Correct answer is Option (a)

Q: Let X,Y⊆UX,Y⊆U. Suppose that n(X)=26n(X)=26, n(Y)=24n(Y)=24, and n(X∩Y)=20n(X∩Y)=20. How many…

A: To derive the number of elements in the set X' union with Y , from the given data

Q: The value of A™ or h in Simpson's Rule is b-a O (b-a) n b-a

A:

Q: S that is closest to b.

A:

Q: Find f, and f, and evaluate each at the given point. f(x, y) = e*y?, (In 9, 2) f(x, y) = 5,x, y) =…

A: We have to find the first partial derivatives of the given function.

Q: EF C and 0 are subsets of Y, then %3D

A: Solution for 6: Given C and D are the subset of Y. We have to show f-1(C)-f-(D)=f-1(C-D)

Q: Given that A = (1, ß, 1), and B = (1, 1, B). If A and B are normal to each other, ßis а. -1 O b. 0.1…

A: The two vectors are given as: A=1,β,1 and B=1,1,β Also, A and B are normal to each other.

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.