Let n, k, m EN with n2k21. prove that

Q: Show that Y has a CDF that is U(a,b).

A: a. Show the graph of the probability density function of Uniform distribution. From the given…

Q: Let A=(1, 0), B=(0, 1), C=(1, 1), and D=(r, 1). Verify that R(A, B, C, D) = r.

A:

Q: Show that Sn is solvable when n ≤ 4.

A: Given: Sn. We have to show that Sn is solvable when n≤4.

Q: Let A, = {..., – 2,- 1,0,1,...,i}. Find

A: Ai={..., -2, -1, 0, 1, ......, i} ∩i=1nAi=?

Q: and -5 Compute ū - v. 2

A: Given    Formula :

Q: 9. Express the gcd(117,213) as a linear combination of s and t such that gcd(117,213) = 117s + 213t…

A: To write the gcd(117, 213) as a linear combination.

Q: Let R = [1, 2] × [1, 2]. Compute ye*"dA. R

A:

Q: 3. Which of the following statements are true? There may be more than one correct answer. A. Ø CA B.…

A:

Q: Let S = {(1, 0, i), (1, 2, 1)} in C3. Compute S⊥.

A: For the given space in C3 let the desired perpendicular space be (a,b,c). It follows the conditions…

Q: Let _X=R². Find M² if M= {(a,1)}.

A: Given that, Let X=R2 Find M⊥ if M=a,1.

Q: Show that S = {x* + 1, xª + x, xª + a², xª + æ*, xª} spans PA.

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Q: Show that A × B ≠ B × A, when A and B are nonempty, unless A = B

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Q: Show that gcd(a,n)=1 if these exist m and k such that ma+nk = 1.

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Q: Compute u – 3v, u v and u x w.

A:

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

A: Dot product of perpendicular vectors is 0.

Q: Determine s, t eZ where gcd(222, 921) = 222s + 921t.

A: I have used division algorithm to solve the problem

Q: Let A={2,y,z} and B={3,x,z}. How many distinct elements are in (A×B)∩(B×A)

A: Given, A={2,y,z} B={3,x,z} How many distinct elements are in (A×B)∩(B×A) ?

Q: 2. Prove that Qn [2, 3] ~ N.

A: Two sets A and B have the same cardinality if there exists a bijection (onto , one-to-one…

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

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Q: Let ü = 21 – k and i = i + 3j + k. Compute |ū], |ū], ū × ĩ, and Projzu.

A:

Q: Create w = (1,3,5,..., 29). Give your R-code to subsequently remove all the components greater than…

A: R-code for the above problem is given as below: w= seq(from= 1, to= 29, by = 2)ww_remove <-…

Q: d. Find E[YOY] for n = 0,1,2 e. Find Cov[YoYn] for n = 0,1,2 f. Find E[YkYk+n] for n = 0,1,2

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Q: Find a number z (except 0) such that Az³ + Bz²+ Cz = D 2 1 3 0 -2 -4 00 ^-[ ] ³-R2 :]-[+]-[1] B= 1 2…

A: Solution

Q: if n(A U B) = 97 and n(A) = n(B) = 69, find n( A ∩ B)

A: We are asked to find n(A∩B)

Q: Let z = 2 - 3xy?+ x². Zay %3D Zyy

A:

Q: Suppose that B is a point between A and C. Prove that AB−→ =AC−→

A: B is a point on AC. Let, A=(x1,y1) and C=(x3,y3)Then direction vector of AC=(x3 - x1, y3-y1)

Q: For what values of aand b is {u, v} an orthonormal set?

A: A set of vectors form an orthonormal set if all the vectors in the set are mutually orthogonal and…

Q: 1) a. The number of mobile phones made by Finland has the following probability distribution: А 2 +…

A: