Theorem 3-11. If A and B are two events with positive probabilities {P(A)± 0, P(B) *0}, then A and B are independent if and only if P(A OB) = P(A). P (B) ...

Q: prove a Bolzano–Weierstrass theorem and explain on how you prove the theorem. Thank you

A: Solution:-

Q: Find la da without using the Fundamental Theorem of Calculus.

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Q: Prove the absorption law of x + xy = x using other laws of identi

A: to prove x+xy=x x+xy=x1+y use the identity law x+0=xx·1=x hence,  x+xy=x·1+x·y

Q: Derive the De Moivre's Theorem with detail Explanation?

A: Statement: For any real number x, we have (cos x + i sin x)n= cos(nx)  i sin(nx) Or, (eiθ)n=eiθn…

Q: 1 2 3 1 1 2 0 1 2 Let A = Find A5.

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Q: 5. (6 + 15i ) 3

A: this is a problem of complex analysis.

Q: Complete this following proof in its proper format:   Proof= { (∀x)(∀y)(Rxy->Rxy), (∀x)Rxb } |-…

A: The given statement is  ∀x∀yRxy→Rxy,∀xRxb|-∀xRbx. we have to prove the statement in the following…

Q: Prove: If a > 0, then (1/a) > 0.

A: It is given that a> 0.It is known that if ab > 0 then a > 0 or b > 0 or a< 0 or b…

Q: #1 part j

A: For question 1 part j: To show that for real values x, y If 0<x<y then 0<1y<1x

Q: he following table shows the value V, in dollars, of product t years after it is purchased T | 0 | 2…

A: Here in the given question, there are 4 observations and the cost in dollars V is decreasing and…

Q: Show that A = has two different factorizations of the form A = L · U where L is lower triangular…

A: Given: A=0001. To show: A has two different factorization of the form A=L·U, where L is lower…

Q: best Rank 2 approximation F ind weth respect to I|F|l the where to A -1 2 -1

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Q: asigma algebra 2. over X ? pcove your answer. Prove your

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Q: 6. Prove that "x² dx = b³a³ 3

A: If F(x) is the anti derivative of f(x) in the interval [a,b] then

Q: Xn+1 axn_b+Yxn-k -1 (xn−b)ª−¹+y

A: Given: The information showing the proof of a specific theorem.To prove: xn+1=αyn-b+γxn-kxn-bq-1+y…

Q: Show that 2 is a unit in Z₁5 by finding its inverse.

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Q: Find inverse Laplace by residue theory 2. XeS+(て-2x。) s- 25+5

A: Find the Laplace inverse transform by residue theory L-1x0s+x1-2x0s2-2s+5

Q: 2. (– 13 + 3i)31

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Q: 4 Jxdx = 1

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Q: State and prove the two versions of fundamental theorem of calculus. Discuss the significance of…

A: Solution :-

Q: How about for question 2? Proving F

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Q: Show that 1 + 3x is a unit in Z9[x].

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Q: Examle show thet bhe fencbion s esechu=-sechurben he de

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Q: 1. (10 + 7i )®

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Q: MA Let r [-1. 1] and F(x) = f, f(t)dt. where the function f is defined by 1. if x > 0. f(x) = { 0.…

A: f is not continuous at x=0.