If X ∼ N(2, 9), compute a) P(X ≥ 2) b) P(1 ≤ X < 7) c) P(−2.5 ≤ X ≤ −1) d) P(−3 ≤ X − 2 < 3).

Q: Q3 Prove that In Coth x 1

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Q: Solve for r: In(x) + In(x + 2) = 3

A: Use the properties of lograthim and simplify.

Q: 4. Show that if ki = (X; – X)/[Σ(X; – Χ)2], then (a) Σ ki = 0; = (b) Σk? = 1/[Σ(X - X)]; (c) Σk;(X;…

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Q: 2. Using OLS or any other suitable method, Prove that E(ß1) = B1 E(ßo) = Bo

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Q: 12. What can you conclude from (PV Q) ^ ¬P? Prove it.

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Q: 3/4 Given: 4 2x+ 35 Prove: x= 4

A: Given: 42x+34=35

Q: 4.1c. Show that the product of two integers that can be represented by x2 +dy?, is always another…

A: Prove that the product of two integers of the form x2+dy2 is always of the form x2+dy2. Consider two…

Q: The value(s) of x that satisfy In(x² + 1) – 2 In(x) = In(16) – In(8) are/is

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Q: Find b fa@ dk and if if x iN rofional ニ :X if x is irrational if x is rationa l if a is irretional り

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Q: 6. Show that, for integer s, S. s! | x25+lexp(-ax²)dx =: 2a +1

A: Note: Given proof statement has a little mistake, I have proof the actual result. First i have…

Q: which of the folowiny -xト! is -3x 2 へ pove seies fore =e.e e E (-)"(-3x) n ハン 0 37 B. e (3x)" nこO *ス…

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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&gt;x and y&gt;z. Now we want to show…

Q: of Voots of the equation. 2x+3X+5=0 is The muttiple is Ę 2. 3 Prove That The sum

A: Use the formula for the sum and product of the roots of a quadratic equation.

Q: +prove by indirect method that if X+y>5 then x>2 or

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Q: 2. Is * commutative? If it is commutative, show it. Otherwise, give a counterexample.

A: Given, * a b c d e a a b c d e b b c a e c c c a b b a d b e b e d e d b a d c

Q: Let w be defined as 2 more than the number of digits in the integer w. For example, 15 =4(2 digits…

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Q: 1] Let X,YER. Prove that VxVy(4x+9y>9⇒(x>5/4 Vy> 4/9)) using method of indirect proof.

A: Prove that ∀x∀y4x+9y&gt;9⇒x&gt;54∨y&gt;49, where x, y∈ℝ. Prove the statement using method of…

Q: Use Simpsons 1/3 rule to evaluate of e-x2 over the interval 0.2 to 1.5 using 6 segments ?

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Q: Prae that x4 -5x +3 is ineducible ouer Q

A: Given polynomial is f(x)= x^4 -5x^3 +3

Q: Show that any positive integer n with n ≥ 4 can be expressed as n = 2x + 5y where x ≥ 0, y ≥ 0.

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Q: Suppose: n ≥ 3 and x,y ∈ Rn , |x - y| = d > 0 and r is some +R, Need to show: 2r = d, there is…

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Q: 1 Show that n2 + 1 IN V

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Q: 3. Evaluate using convolution theorem: ਕਰ S(514)

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Q: ² = 4. Maximize Q = 4xy, where x and y are positive numbers such that x+y %3D y: (Type an exact…

A: topic - application of derivatives

Q: Theorem = 7 K 51 M 25

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Q: If in a AP the sum of m tern=ms is equal to n and the sum of n terms is equal to n ,then prove that…

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Q: Prove that (0.01)(100sin2π(5000)t)2 is equal to 0.5+0.5cos2π(10000)t

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Q: Uつ40+OLU 1ontい し いun 人 の-メS1-Xメーメを interval 3. 3. poutnd to factor p) いUtas0 -use the test -Point…

A: Let's find.

Q: 9:Find the absolute exlemum Verlues of flx) x²-4x+24 over the interNal Cl,41

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Q: FOR N=195, by fermat's theorem an-2 =

A: Given: FOR N=195, by Fermat's theorem an-2

Q: Suppose x, n ∈ N and n not equal to  0. Then, show that xn is positive if and only if x is positive

A: Given that x, n∈N and n≠0. According to question, N=0,1,2,3,4,5........ First suppose xn is positive…

Q: Supposernc N and n 4 0 Then show that rn is positive if and only if r is positive

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Q: 4. Sketch the proph of the following funcfions; メーメ+4 (x+4 a) f(x) = (x+4) x b) gex) = %3D

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Q: 1 Use convolution theorem to evaluate L-1 (s²+9)²)

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Q: If (ar + bx) = 4n and n+1 k-1 (ak-br) = then ar = n+2 k=1 k-1

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Q: Given: 5(2x – 8) = 30; Prove: x = 7 -

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Q: (3) Let A be m x n (not need to be square). What is the sum of the diagonal elements of ATA in terms…

A: (3) Given that Abe m×n matrix (not need to be square matrix). We have determine the sum of the…

Q: Suppose X~N(113,18), and Z~N(0,1). Then x = 94, is equivalent to z = ______.

A: Given that, Suppose X~N(113,18), and Z~N(0,1). Here, mean μ=113 and standard deviation σ=18

Q: In yz can be written as : 1 In x - In y + In z a O 4 1. In x- In y- Inz b O 4

A: I have Provided this answer in step-2.

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

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Q: B increases as µ approaches from µo, when Ho is false True or False

A: Given problem Given that   B ( β )  increases as μ approaches from μ0, when Ho is false . Ans)…

Q: Show that if ƒ′′&gt; 0 throughout an interval [a, b], then ƒ′ has at most one zero in [a, b] . What…

A: Given:

Q: 4. Show that if ki = (X; - X)/[Σ(X; – X)2], then (a) Σki = 0; = (b) Σk? = 1/[Σ(X; − x)2]; (c) Σκ;(X;…

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Q: 9 show Itat Ihe maclayvin Sevies For Hense is メ+ メ t.. 4- X

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Q: O s//n O olVn n1 n2 O O O O

A: We have to choose correct answer for standard error from given data.

Q: Suppose n (a)= 7a + 4, determine a such that n (a) = 39. %3D

A: GIVEN n(a) = 7a+4 and n(a) = 39

Q: 2.2 Use algebraic manipulation to prove that (x +y) · (x + y) = x.

A: As 2 Questions are given, I will solve only the first, We need to Prove that: x+y(x+y¯)=x Solving…

Q: If p,q,r are prime number but p is not equal to q, then what is gcd(p,q)? What is the smallest…

A: It is given that p and q are prime numbers. Assume that gcdp, q=d. Then, d is the greatest common…

Q: 8. Working over R, suppose that M = PDP ' where P 1 Then, for any positive integer k, we have that…

A: To find Mk =?

Q: 6n_ and If (ar + bx) = n+1 k-1 , then 1 (ak – br) = 712 n+2 k-1 k-1

A: If ∑k=1nak+bk=6nn+1 .......................(1)  and  ∑k=1nak-bk=nn+2-1n ......................(2) we…