(i) If X is a random variable and K is a constant, then E(X + K)= E(X) + K

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: Prove that (1, 2) (1,(1), 2, 3).

A: We know, if A and B are two sets then, A is subset of B  if every element in A is also in B.

Q: Use De Moivre's Theorem to find the fourth root of Z = 8i(3 + v2).

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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: Define the Rolle's Theorem?

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Q: From Leibnitz theorem °C=

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Q: Prove that

A: Given that ∫461xdx

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

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

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Q: Sketch the following given that Z = x + yi (2-3) (2+3) = 2

A: Given ,                 (z-3)(z+3) = 2   ;    z=x+iy

Q: 2 2 X = {K_EW : S" (Lu' (+)/² + 9 ª 14(+)1³)dt< =0} O why this is inner Product ?

A: Given: X=u∈W:∫0∞u't2+92ut2dt&lt;+∞   To explain: Why the given condition represents an inner…

Q: 2. (– 13 + 3i)31

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Q: What are the various applications of the dot product?

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Q: 4 Jxdx = 1

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Q: How about for question 2? Proving F

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Q: Explain Drac Delta functoo

A: Given The given function is 'Dirac delta function'.

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

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Q: Prove (A N (B U C) = Ā U (B U C) %3D

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Q: Use part one of the fundamental theorem of calculus to y = 3x + 7 t 1 + 1³ dt

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