3. What are the restrictions on x?

Q: 1) Evaluate whether y, and y, are uncorrelated 2) Evaluate whether y, and y, are independent

A: Given, y1y2 = 111-1x1x2 So,  y1 = x1+x2y2 = x1-x2 And, Mean is 0 and Variance is 1 So, E(xi) =0…

Q: How to determine The direchon that the arrow at the pout 6,1) at he eghahión of he 1t arder g'=…

A: find the slope of the equation  at particular  point Example : y'=y-2x Take x=  0     0      0     0…

Q: Let S = Span}( 3 2 3 . Show that dim(S)=2. 3

A: Basis: Let V be a subspace of ℝn. A basis of V is a set of vectors v1, v2, ..., vm in V such that:…

Q: If A= then A" + nl is equal to

A:

Q: Suppose is dhe iavene faction of a diffarentiable šunc- tica fand let Glu) -1/r . E3) - 2 and /3) -…

A: G(x)=1f-1(x)f(3)=2 , f'(3)=1/9

Q: (a,b) is measurable.

A: (a,b) is an open interval.  Open intervals are measurable.

Q: Let X-Bin(5,0.5), then P(x >3|x >2) is

A:

Q: Suppose you are given four natural numbers w, x, y,z e N such that w>x and y > z. Show that ly – w|…

A: It is given that w, x, y, z are natural numbers such that w>x and y>z. Now we want to show…

Q: 6. li Q-ん

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

Q: Prove that (X + Y) (X+Y) = X

A:

Q: HeW. By the Same way Prove that: X Ju (x) (X)

A:

Q: 3 10. Show that R² span

A:

Q: (b). lim zInz² et

A: To evaluate: limx→0 xlnx2ex Using logarithmic property we can write the given limit as  limx→0…

Q: If Z = eax + by F(ax - by); the value of %3D az is + a ду az

A:

Q: 11. If |A| = 3, how many relations are there on A?

A: Given A=3

Q: find rank(AT) and nullity(A)

A: Rank of A = rank of A^T use this relation

Q: What is the dimension of P,?

A:

Q: Notice that h is definec this.)

A:

Q: that prove

A: Given, D⊂R2 be a disk containing the origin and g:D→R is a  function given by…

Q: At Lana's bake sale, 2/3 of the brownies were purchased by 5/7 of the customers. If there were at…

A: Let X be the number of brownies and Y be the number of customers. It is given that 2/3 of the…

Q: H-) in Limits 3-3- 2.21 9 iaam

A:

Q: Prove that if x+y=%30 then y=-x

A: See the attachment

Q: (a, b) is measurable.

A: The answer is given as follows :

Q: 3. Show that Z, -

A:

Q: If xly, then show that ||x+ y|| = ||x- y|!.

A:

Q: What is Rolles Theorem and how do you find "c"?

A: What is Rolle’s Theorem and how do you find c

Q: Let X-Bin(5,0.5), then P(X >3|X >2) is

A: Given information: Given that the random variable X follows binomial distribution with parameters n…

Q: is this a fucntion or not. given its domain and range   {(1,1), (2,2), (3,3), (4,4)}

A: This is a function.

Q: Show that if x is in both W and W-, then x = 0.

A: Dot product of perpendicular vectors is 0.

Q: Consider the following theorem.

A: Given, Where, And We have evaluate the integral,

Q: ху • prove that x +y Example If z = az dz + y.- Əx х. ду

A:

Q: (a, 0) is not measurable.

A: In this question, we check the given set is measurable or not. here we use the condition of Lebesgue…

Q: Let S = {2x, 1 –- x, x2 + x- 1, x + 1}. Then S is a %3D

A: for a basis we need to check that a set must be linearly independent and spans the whole vector…

Q: a) What is the support set of X? b) Write out the PMF of X. c) Compute E[X].

A: Cumulative Distribution function (CDF) : The cumulative distribution function of a discrete random…

Q: have the following properties:

A:

Q: Prove S^2 is simply connected.

A:

Q: 5. Demonstrate that Im(iz) = Re(z).

A: It is required to demonstrate the problem 5. Problem 5 is solved below in detail.

Q: H-W Limits 3-3- १.२। 9 iaam in

A: We will find the limit .

Q: Theorem 5 there is auniqe Reul for X=2 Sit X ER

A:

Q: Oct 31, 2021, 16:44 Problem-2 0 Let foo = x?-2a and gcauz VI-x 6) is q CG (-Z)) defined! domain ind…

A:

Q: If f(x 1.,„,) = g(ê,e) h(x,...,, then ê is Select one: a. efficient b. consistent C. unbiased d.…

A:

Q: c) Evaluate ſ x*(In x)²dx

A:

Q: what is a phythagoras theorem?

A: Pythagorean Theorem has a right angle triangle.

Q: prove the following:

A: Given,           f(x-y, x+y)=2(x2+y2) To prove that,          ∂f(x, y)∂x+∂f(x, y)∂y=2(x+y)

Q: - How many modes does X have?

A: The probability function of X can be described as X 1  5 10 15 f(x) 24k 100k 150k 150k

Q: (a, b) is measurable. صواب ihi

A:

Q: Compute (x – 2) for the following set of n = 7 values. X1 = 8, x, = 15, x3 = 14, x4 = 10, x5 12, x6…

A: Given,   =?

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.