Let p». Prove that, for every e > 0, a.a.s. the largest component of G(n, p) has size at least (1-)n.

Q: (X- Example 9-31. If X ~ N (µ, o²), obtain the p.d.f. of : U

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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: Draw the Venn diagram with the following information: ANBNC={√2, √-1}, (ANB) NC'={2%, 00}),…

A: Here we eight disjoint parts , putting into them we can construct ven diagram

Q: If Z ~ N(0,1), compute P(Z2 < 3)

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Q: h3 The degree of precision of a quadrature formula whose error term is : f"() is 24 а) 1 b) 2 c) 3…

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Q: Find ||uLy|| in Figure u= (3, 5) = (8, 2) P. FIGURE

A: v=(8,2) u=(3,5) uv=?

Q: Let ECR. A point a E R is called a cluster point of E if En(a-r, a+r) contains infinitely many…

A: Given: E is bounded infinite subset of ℝ. To prove: E has at least one cluster point.

Q: Find the set of ordered pairs (T0, Yo) for which Picard's Theorem guarantees that the IVP y ry %3D y…

A: Given,            y'=xyx+y, y(x0)=y0

Q: Let U1, U2, U3, .,U48 be independent and identically distributed U,~Unif(0,1) and X = U, + U2 + U3 +…

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Q: Prove that if gcd (a,b)=1>then gcd (ab,ab)=l

A: I have proved using the fact that gcd can be expressed as integers linear combination q

Q: Consider the subspaces U = ((1, 0, 0), (0, 1, 1)) and W = ((1,2,3)) of the vector space R³. [Note:…

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Q: find the'mters ection d Exe sy,z]= [a,0,31++ 4,-2,178 [+sy,z]=[6,-12,--11]+5 [1,2,4]?

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Q: * /Q1 = V4 – vx are: The domain D; and the range Rf of the function f (x) : D; = [0,16], R; = [0,2]…

A: Let's find given function domain and range.

Q: Exercise 4. Suppose TE L(V) is normal. (a) Prove that range T = range T*. b) Prove that null T* =…

A: Given that T∈ℒV is normal.  To prove that range T=range T* Since T is normal, for all v∈V, Tv=T*v…

Q: PROVE THE STATEMENT "There exists a, b ∈ Z+, such that if a > 1 and b > 1, then gcd(a, b) > gcd(a^3,…

A: Given statement is wrong because there is no a, b ∈ Z+, such that if a &gt; 1 and b &gt; 1, then…

Q: xʻy Let f (x, y) = if (x, y) # (0,0) and f (0,0) = 0. (x4+6y8) r4.

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Q: Find a and b such that 3 1 1 27 = a -3 + b -6 2 a = b =

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Q: Suppose that set A has 4 elements, set B has 8 elements, and their union has 9 ele- ments. If the…

A: Given that, Set A has 4 elements Set B has 8 elements Union has 9 elements Universe U has 18…

Q: (8 (10 pay x/x = (x+x)= xpe (1)3-x 21-AIBALI only one

A: As per bartlby guidelines we can answer only first question and rest can be reposted

Q: 2. Show that if a]b then a'|b² for all integers a and b (Symbols V, 3, A, V, V,A,→,-)

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Q: · (b + c) = a · = a · b + a · e for all a, b, c € R³. . 7. Prove that a.

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Q: Q3)) Let (Z8, +8) and H=(0,2,4, 6} .Find the normalizer of (H, +8) in (Z8, +8).

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Let a ∈ G be such that |a| = ∞ . For m≠n prove that a^m ≠a^n

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Q: a. Show that by using Laws that if the compound statement is logically              equal.…

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…