Assume that Pr[E]=0.65Pr[E]=0.65, Pr[F]=0.35Pr[F]=0.35, Pr[G]=0.6Pr[G]=0.6, Pr[E∩F]=0.15Pr[E∩F]=0.15, Pr[E∩G]=0.35Pr[E∩G]=0.35, Pr[F∩G]=0.25Pr[F∩G]=0.25, and Pr[E∩F∩G]=0.1;Pr[E∩F∩G]=0.1;. Find the following probabilities: (1) Pr[E′∩F′∩G]=Pr[E′∩F′∩G]= (2) Pr[E∪F∪G]=Pr[E∪F∪G]=

Q: assume that Pr[A′]=0.55, Pr[B]=0.35 , and Pr[A′∩B]=0.2. (1) Pr[A∩B]=Pr[A∩B]=   (2)…

A: Solution : Given information; P(A')=0.55 P(A)=1-P(A')=0.45P(B)=0.35 and P(A'∩B)=0.2

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Q: 3) Let f(T) e R[T] be a polynomial of degree > 3. Show that there exists polynomials g(T) and h(T)…

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Q: Let f: X→Y be a function, and let A,BCY. Prove or disprove: f-¹(A)uf-¹(B).

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Q: determine L−1[F].

A:

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Q: assume that Pr[A]=0.25Pr[A]=0.25, Pr[B]=0.35Pr[B]=0.35, and Pr[A∩B]=0.1Pr[A∩B]=0.1. 1)Pr[A|B] =…

A: Given: P(A) =0.25 P(B)=0.35 P(A∩B) =0.1

Q: Let f: Z → Z be defined by f(x)=x²-1, and let C = {0, 1, 3). Find f(C), f-¹(C), f(f(C)) and…

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Q: Let f : Z+ → N be the floor function f(x) = [(x – 1)/2].

A:

Q: (d) Show that T is bounded and find ||T||. (e) Find the adjoint T* of T.

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Q: Find ||F||. F(x, y, z) = i + j + k

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Q: Prove that P[X |Y ] = (P[Y | X] · P[X] ) / P[Y]

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Q: Assume that Pr[E]=0.5Pr[E]=0.5, Pr[F]=0.65Pr[F]=0.65, Pr[G]=0.45Pr[G]=0.45,…

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Q: Assume Pr[A]=0.3, Pr[B]=0.3, and Pr[A∩B]=0.05. Find the following values: 1. Pr[A|B]=  2. Pr[B|A]…

A: Note: Hey there! Thank you for the question. As you have posted multiple sub-parts, we have helped…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.