Show if gcd(a, b) = 1 and a \x and b\x Then a b\x

Q: (a, o) is not measurable.

A: to find that a,∞ is measurable or not  proceed as follows We know that every interval is measurable.…

Q: 3. Prove that (An B)² C A × B.

A:

Q: Show that [x, p;] = iħ.

A: note :  As per our company guidelines we are supposed to answer ?️only one question. Kindly repost…

Q: 6. Prove that if gcd(a , b) = 1, then gcd(a + b, ab) = 1.

A: We need to prove that if gcda,b=1 then gcda+b,ab=1 Let us on the contrary assume that  gcda+b,ab=c…

Q: Show that if gcd (a, y) = 1 and a \ xy Then a\ x

A: Definition : Greatest common divisor ( gcd): Let  a and b be are two  integers, not both 0.  A…

Q: let f:(a,b)→R be de fined by X€QN(a,b) x€Q' n(a,b) -2 f(x)=' 3

A: This is a problem of Differential Calculus.

Q: Show that if a\b and gcd(b, c) = 1 Then gcd(a,c) = 1 %3D

A:

Q: (a,b) is measurable.

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

Q: Let A = {x ∈ Z | 6 divides x} and B = {x ∈ Z | 3 divides x}. Prove that A ⊆ B, and then prove that…

A: We can prove using like showing every element in one set is an element of another set like that.

Q: Example 38.18. Prove that (a) div A, = VgA)

A:

Q: Prove the A.B = B.A.

A: To prove AB = BA.

Q: 2. Show that cÃ=cA.

A:

Q: Let H„(x) = (-1)" -w that h, E L² (R). , x € R, n E No, and let h„(x) dan e H„(x)e¯

A: Given: Hnx=-1nex2dndxne-x2 x∈ℝ, n∈ℕ0 This is a Hermite polynomial function. hnx=Hnxe-x22 To…

Q: 4. Let a,b,c € Z where c | (a+b). Prove that gcd(a,c) = gcd(b,c).

A:

Q: Let X~U (0,0), then P(X > X²) is

A: Given that X~U0,θ fx=1θ-0=1θ, 0≤X≤θ

Q: Show that if E1 and E2 are measurable, then m(E U E2) + m(E1n E2) = m(E1) + m(E2).

A:

Q: Prove that A CB P(A) C P(B).

A: We have to prove that

Q: If a and b are even then GCD(a,b) must be 2

A: Given statement :- if a and b are even then GCD(a,b) must be 2

Q: Let f:[a,b]→ R. Which of the

A: Given, f:a,b→ℝ. The function f has domain in the interval a,b and has range in set of real numbers…

Q: prove that erf (x) dx =o

A: To prove: ∫−aaerfxdx=0

Q: Show that if gcd (a, y) = 1 and a \ xy Then a \ x

A: if 1. gcd(a,b)=1then there exist some integers m and n such that am+bn=12. suppose a and b are…

Q: Prove that |A U B| + |A n B| = |A| + |B|

A: Let A and B are two sets. A = number of elements in the set A. B = number of elements in the set B.…

Q: Exercise 2. Prove that if A = B and C z D, then A × C = B x D.

A: Given data: A≈B......(1)C≈D......(2) The objective is to prove A×C=B×D

Q: 10.

A:

Q: (a, b) is measurable.

A: The answer is given as follows :

Q: If A ⊂ B, can A and B be independent under any circumstances? Explain

A:

Q: If gcd(a, c) = 1 and gcd(b, c) = 1, prove that gcd(ab, c) = 1.

A:

Q: Show that (a) Cov(aX, bY)= ab Cov(X,Y). (b) Cov(X+a, Y + b) = Cov(X,Y). (c) Cov(X, aX+b) = a Var(X).

A: Let (X ,Y) be a bivariate random variable and a, b be real constants. Covariance measures joint…

Q: Show that if a \ b and gcd(b, c) =1 Then gcd(a,c) = 1

A:

Q: Show that if AB={0}, then P(A)≤P(B).

A: Given that

Q: Show that if gcd (a, y) = 1 and a \xy Then a\ x

A:

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: Prove (A = B) = (A v C) = (B V C)

A:

Q: Let C ~ Cauchy(0,1). Show that C² + C-2 =9 4C² + 2.

A: c^2+1/c^2 >2 thats why it is equal to 4c^2+2

Q: If x]y then gcd (x, y) = y. إختر واحدا: Las O

A: Given x|y hence y=ax It implies that y is a multiple of x

Q: Let Find A = {x E R-1 ≤ x ≤ 4}, B = {x ER| 4 ≤ x ≤ 6), and C = {x E R/3 < x < 5}. AUC {-1, 2, 3, 4]…

A:

Q: Show that if X gamma(r, A) and Y ~ gamma(s, ) independent, are then X + Y is gamma(r + s, ).

A: X~Gammar,λ fx=λrΓre-λxxr-1,     x&gt;0, r&gt;0, λ&gt;0 Y~Gammas,λ fy=λsΓse-λyys-1,     y&gt;0,…

Q: Find conditions on a, b, c, and d such that AB = BA

A: , We need to find the values of a, b, c and d such that AB=BA

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: Find conditions on a, b, c, and d such that AB = BA

A:

Q: dat b)

A: Domain =Value of xRange = value of y a. Domain x∈-∞,∞   Range y∈-∞,∞b .Domain x∈-4,3  Range y∈2

Q: Let X=(1,0, – 1,- /2)'. Then, ||X||, = Select one: а. -V3 O . 2+V2 C. -V2

A:

Q: Consider a LU factorization of 3 A = 6 as A=LU. Then L2,1 and U1,1 are respectively equal to

A: solution:-

Q: Show that a) A − ∅ = A. b) ∅ − A = ∅.

A:

Q: Show the Complete S lu fwn i 3 ナ *

A:

Q: Show that A ∩ B = A ∩ C need not imply B = C.

A: Let, A= {1,2,3} , B= {2,3,4} and C= {2,3,5}

Q: prove that a(a+b)=c(c+d). a b d

A:

Q: 4. Let a,b,c E Z where c| (a+b). Prove that gcd(a,c) = gcd(b,c).

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.