6. Sketch the set X = {(x, y) E R? : y

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

A:

Q: The Critial Points of fcx,y)t+Ý-4y subject to the x+y=9 is O (o,さ3), (は5,2) ④ (e, さ)さ何,) None of…

A:

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 S = { all (x, y) with æ and y rational numbers j. (a) What is the interior of S ? (b) What is…

A: We know interior of the set of rational numbers is empty and boundary of the set of rational numbers…

Q: 1. Show that S, has the presentation (x, y|x² = y = (xy)² = 1). %3D

A: The symmetric group S3 is given as S3=I, 1 2, 1 3, 2 3, 1 2 3 1 3 2 where  I=123123, 1 2=123213, 1…

Q: Let X=ℝ2 and define d,:ℝ2×ℝ2→ℝ d2((x1 ,y1),(x2,y)2)) = max{|x1 - x2|,|y1 - y2|}. Draw the…

A:

Q: nners who compete in marathon races are described by the join 0<x, y < 1, f(x, y) = (4xy, 10,…

A:

Q: Use the following rule in mathematical morphology to fill the holes inside the image A to be black.…

A:

Q: Q4/Find Loplace transtorm of £(4)= et by using} defining fanotion ر م ) ) st e" dt

A:

Q: If I, = [x^tan"x dx, Prove that (n+1), + (n-1),,2 ° п 1 %3D 2 n

A:

Q: T C S E

A: Answer is : Yes

Q: o Show that X2 = {(x, y) E X x X : x<y} is a sublattice of X x X. %3D

A: Given that X is a lattice. To show that X[2]  is a sub lattice of X×X. It is enough to show that,…

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: S :R\{0} → R, S(r)=e4z^+5z=2–1

A:

Q: Given sets X and Y. For x EX and for y E Y, we form the Cartesian produc X x Y := {(x, y) : x E X, y…

A: Given that: X={-1, 1}Y={-2, 0, 2}

Q: In which of the following cases is the mapping x: R² → R³a patch? (а) x(и, v) — (и, uv, v). (c) x(и,…

A: A mapping defined from x : R3 to R2 is defined a patch if x maps U diffeomorphic ally onto x (U) As…

Q: 1. Sketch the following sets and determine which are domains: (a) \z – 2+ i| 1; (e) 0 4; (d) Im z =…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: [2 Lo 2. and defined T: R² → R³,by T(X) = AX. Let A Find the images under T of u = |E|, and v =

A: Given a linear transformation T:R2→R3 by T(X)=AX where A= 2002

Q: Sketch z =- 2cos y in R3

A: The expression y=cos(x) will give the graph of a cosine curve in the x-y plane, with the value of y…

Q: Q/ show thet f(2) = 2+ Conformal maps 121= 1 ? on

A:

Q: 4. If X and Y are independent RVs, then O2+ ,(@) = ¢,(@) × ¢,(@)

A:

Q: 10. Let ro = all points (x, y, z) for which (xo, yo, zo) and r = (x, y, z). Describe the set of %3D…

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

Q: and Z , if y=0 Solue %3D By using Direct melh oel.

A:

Q: Let X; ~ X"(1) i= 1,2, . - ·, n and assume they all uidependent are Y = Ź Xi %3D しニ」 ان منتتفينتمنل…

A: Given, Xi~χ12 ,i=1,2,...,n a. Y=∑Xii=1n Therefore, X1+X2+.....+Xn~χn2 above is possible using…

Q: et X~U([-, 1) and let y = tan(r), show that y Cauchy(0, 1)

A: # using Jacobian transformation we have proved that y=tanx follow Cauchy distribution (0, 1)

Q: az Find if yz – In z = x + y ax 3.

A: We have              yz-lnZ=x+y

Q: The area bounded by the curve y = 7x and the lines z= 2 and =9 above the z-aris is O 539.00 square…

A:

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

A:

Q: Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find ∂z/∂t.

A: Solution:- The given question is  Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find…

Q: c If in is an involution of X, show that (x, y)in = (yin, xin) is an involution of X2). %3D

A: Let X be a lattice We have to show that (x, y)in=(yin, xin) is an X[2] X[2] is a 2 x 2 matrix We…

Q: 11.1. Find images of the following sets under the mapping w = e² : (a). the vertical line segment x…

A: As per our guidelines we are supposed to solve only first three subparts of the problem. For the…

Q: Let a and b be nonzero and f(x, y) = (ax + by)e-x Show that if a ± b, then there are five critical…

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: 8.Prove the following relationships: a) I(X,Y)=H(X)-HOX/Y)

A: Solution

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: If w = f(u, v), u = x + y, and v = x - y, show that w,wy = w - w?. %3D %3D

A:

Q: {S := n(x, y) | 2x + 3y ≥ 12}

A: First we draw the line then find the region.

Q: Draw the region of z that satisfies the following cases. a) z-2i| 2

A: We need to find the equation of curve for the given problems in two-dimensional real plane and then…

Q: For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by fX,Y (x, y) = x + y/21…

A: Solution

Q: Let K = Span{ t-t, 1+3t}, then dim K = %3D

A:

Q: Show for all x, y in R |x+ys]xl + ]y!

A: consider left hand side  and use the result x=x2 x+y=x+y2=x2+y2+2xy≤x2+y2+2xy≤x+y2=x+y

Q: Consider the diagram below. W Which of the following statements is correct? A AXYZ~AWVZ by AA…

A:

Q: 3. Show that a reflection a in the x-axis defined by o(x, y) = (x, -y) is an isometry.

A: The solution of given problem is followed by

Q: A subset W of R° is given by = {(x,y, z) | 2x = y = 2z}. (i) Write down the distinct elements of W.

A:

Q: Having aeR and ɛ > 0. Define ɛ-neighborhood of “a"

A: Explanation of the answer is as follows

Q: If p(x, y, z) = x²z + ey/x, evaluate grad op at the point (1, 0, -1).

A: The function is φ(x, y, z)=x2z+ey/x

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.