1. Show that for all z1, Z2 E C, Then we have: |Z1+ Z2| < ]Z1] + |z2|

Q: 1: Prove that (c a) * H = (c b) * H implies that a H = b H

A: Given an equation. We need to prove that : a*H = b*H where H is a subgroup of a group ( say G). Also…

Q: Q3 Prove that In Coth x 1

A:

Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1 + Z2| < |Z1| + |Z2|

A: Using complex properties.

Q: |=1|+ |= 2 | |- |- | 3. If z3 + z,, show that VI +

A:

Q: Let x, y e Z. Prove that if 3x+7y is odd or 5x + 6y is even, then x or y is even.

A: We have given that for x,y belongs to integers. If 3x+7y is odd or 5x+6y is even then x or y is even…

Q: Given: 23 = Z1 Prove: АВ АС 2 3/6 E

A: Given: The angle ∠3 is equal to ∠1. Concept used: If the two angle of a triangle is equal then side…

Q: Prove that if |z| = 3, then %3D 5 2z – 1 7 - 13 4+ 22

A: The given is related to complex numbers. The solution is explained below.

Q: Suppose X ~ N ( u=1, o=2) a) P( X&lt; 1.37) b) P( X &gt;1.37) c) P(X &lt; -1.37) d) P(X = -1.37) e)…

A:

Q: prove using the IVT. √c +√c + 2 = 3 has a solution.

A:

Q: 2- Let z=x+iy. Find a) Img(1/2) b) Re z c) Img (1/z')

A:

Q: Let x, y EZ. Prove that 3|xy if and only if 3|x x or 3 y.

A:

Q: Express y as a fiunetion af k if y - 2r+5, 1- V3t -1, and t- 3k - 5.

A:

Q: Let x, y E Z. Prove that if 3 ł x and 3 ł y, then 3|(2² – v²).

A:

Q: 2. Find three positive integers x, y, and z if their product is 27 and the sum is a minimum.

A: Given three positive numbers are  x, y, and z Product = xyz = 27 And sum is minimum

Q: Show that for all z1, Z2 E C, Then we have: |Iz1| – |z2|| < |z1 +z2l

A: 2) The inequality can be proved as follows:

Q: 5.1. Show that y2 , V2 , and v3 + V2 algebraic. are

A: We will use definition of algebraic numbers

Q: Determine x[2] and x[3] given (a) 2x[n+2] – 5x[n+ 1] = 4n, x[1] = 2 (b) 6x[n] – x[n – 1]+ 2x[n – 2]…

A: Given:  a) b) c)

Q: 11. Suppose A\BC C. Prove that if x E A\C then x E B.

A:

Q: 11.32 question attached. Thank you for answering my question!

A: It is given that X and Y are independent normal random variables.The required probability is:

Q: lar, let m = 2 and n e of A and B such that

A:

Q: 3. Prove that Re(2-+z')<4 when z<1.

A: a.          x+y ≤x + y                                             (triangle inequality)b. Re(z1+z2)…

Q: Show that for n, m e Z+, gcd(2" – 1,2m – 1) = 2gcd(n,m) – 1.

A:

Q: In Let x, y ER" be given. (a) If ||x|| = ||y|| = 1 and x - y = 1, show that x = y. (b) If ||x|| ≤ 1…

A:

Q: Prove that if a, b E Z - {0}, then gcd(a, b) = gcd(a, -b)

A: soln:gcda,b=Greatest common divisor of a and bEvery integer that divides a and bsimultaneously will…

Q: (1) Use the definition to prove that if xn → 2 then (2xn + 1) / xn → 5/2.

A: As per our company guideline we are supposed to answer only first three  qs, kindly post remaining…

Q: Prove indirectly: "V n E Z, 4 ł (n² – 2)."|

A: Ans:Let us assume that 4/n2-2;∀n∈zthen we have there exist a positive integer k such…

Q: 1. Let A = {x E Z | 6 divides x} and B = {x € Z | 3 divides x}. Prove that A C B, and then prove…

A:

Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1 + z2| < ]z1]+ |z2| 2. Show that for all z1, Z2 E…

A:

Q: If A is a 2 x 2 with det(A) = 3, then det(4A1) = %3D

A: det(A-1)=1det(A) det(4A-1)=4ndet(A-1) where n is the order of the matrix.

Q: show that if Z ~ N(0, 1) and Y ~x²(n) with Z and Y to be independent, then T: n

A:

Q: Suppose X~N(112,16), and Z~N(0,1). Then x = 112, is equivalent to z = ______.

A:

Q: Suppose A · B = 0. Show that this implies that C(B) is contained in Null(A).

A: Suppose A.B = 0 then we have to show that  Column space of B contained in the null space of A  i.e…

Q: es lls ew zeiflucifiib ons einiseen stigesber Show that for neN, (2n)! ' (r!)² ((n −r)!)² - 7=0 2n -…

A: We will use binomial expansion to prove given relation

Q: If X is uniform on [-2,2] then p(x <0) = 1 1 2

A: X is uniform on [-2,2]   a = -2,   b= 2

Q: 6. If X has full rank, so that P = X(X'X)-1X', prove that C(P) = C(X).

A: The rank of a matrix denotes the number of independent rows or the number of independent columns in…

Q: (9) Let X z b(n,) and E(3x) = E(3– 5x) find n.

A:

Q: x, and x, in terms of t.) 2 1 -1 1 1 -1 1 2 1 2 2

A:

Q: 4) Let m,n, r E Z with m # 0 + n. Show that gcd(m, n) divides r if and only if there exist a, b E Z…

A: Let gcd(m,n) divides r. Then we have to prove that, a·m+b·n=r Since, gcd(m,n) divides r than by…

Q: True or False? If d = gcd(a,b), then there exists integers x, y such that d = ax +by

A: solution.

Q: Let S = {(x, y) :x² + (y – 1)² < 1} U {(3,0)}. %3D Is the origin an extreme point of conv S? Is the…

A:

Q: x | X> 3) =? and E [X | X> 3] =?

A: X ∼ exp (λ)  having pdf  f(x)=λe-λx      x&lt;0

Q: In Z, let H = &lt;5&gt; and K = &lt;7&gt;. Prove that Z = HK. Does Z = H X K?

A: Given: In Z H=5K=7

Q: Suppose that X ~ Unif(-1,1). Compute (d) P(X = 0.5), (e) P(X² > 0.5).

A: Let ,  The pdf of X is ,  = 0 ; otherwise Our aim is to find the following :  d) P(X=0.5) e)…

Q: 1 If w = f(x, y) = x²y+ \y, then ƒ(÷,x“) is .. 1. O 2x2 2. O 1 3. O 4. O x4 +

A:

Q: D. Is there guaranteed to exist a value of x = c on -2 < c < 2, such that h'(c) = 0? Give a reason…

A: Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and…

Q: Prove the following:  if x^2 = y^2, then x = y or x = -y.

A: Subtract y^2 from both sides.

Q: Show for Re(z) > 1 -dr = r(2) ((2). %3D et - 1

A:

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.