assume that Pr[A′]=0.55, Pr[B]=0.35 , and Pr[A′∩B]=0.2. (1) Pr[A∩B]=Pr[A∩B]=   (2) Pr[A∪B]=Pr[A∪B]=   (3) Pr[A′∪B]=Pr[A′∪B]=

Q: Let X and Y be independent, and let X be N(10, 1) and Y be N(11, 1). PIX >Y),

A: From the given information, X and Y are independent random variables. Let X be a N(10, 1) variable…

Q: 4. Let aj = 9. and b = 63 , a2 = 45 (a) Write b as a linear combination of a1 and a2. b = aj + a2.…

A:

Q: LetP(A) = 0.10, P(B) = 0.20, and P(A∩B) = 0.02. Are A and B mutually exclusive? Justify your result…

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Q: A fair coin is tossed two times independently. Let H₁ = {1₁ (1, if head is obtained at the ith toss…

A: When head is obtained at 1st toss then H1= 1  When head is not obtained at 1st toss then  H1= 0 When…

Q: 17. -4 Compute and compare u•v, u|2, Ivl2, and Ju +v2. Do not use the Pythagorean Theorem. Let u= -…

A:

Q: Let fi (2) = - 5x – 5, f2(x) = – 6x² – 8x – 3, f3(x) = 2a² + 10x + 3, and fa(x) = 2x – 9. Find a…

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Q: verify that (A + B)T = AT + BT

A:

Q: 1. Let Q(v2) = {a+b/2| a, b E Q}. Prove that Q(/2) = Q[x]/(x² – 2).

A: We have to show that isomorphism means there is function ϕ such that we have to show that it is an…

Q: () Let z = x + iy. Find Im and Im 2 in terms of x and y. Im Im z2 ||

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Q: Assume that n(U)=115n(U)=115, n(B′)=65n(B′)=65, n(A∩B′)=32n(A∩B′)=32, and n(A∩B)=19n(A∩B)=19 Find…

A: Now consider,

Q: Using the substitution u = (A) (B) C D 1+1 du [₁ -1/2 du [(u ¹/2 - u-1/2) d du (u - 1) / u-²1) x + 1…

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Q: Which one of the following is isomorphic to Z4 x Z6/((2,4))?

A:

Q: Show that (AB)T and BTAT are equal.

A: Now,

Q: How many solutions does Ax = [1]   have?

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Q: w+y+2z w+2x-y -3 2w+x+3y-2z ] = [X²] 6 x-2y -2 0

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Q: Assume that n(U)=90n(U)=90, n(A)=41n(A)=41, n(B′)=50n(B′)=50, and n(A∪B)=63n(A∪B)=63. Find n(A∩B)

A: