pose that X is a real valued random variable and y: R → R inuous. Show that if X and (X) are independent, then (. t be deterministic (i.e. there is a real number a so that P(½(X) = 1).

Q: Suppose P(A) = 0.24 and P(B’ ) = 0.48   (a) Find P(A ∪ B) if A and B are independent. (b) Find…

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Q: Let A be an invertible matrix. Show that det (adj (A)) = det (A-¹).

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Q: Use a table to express the values o

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

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Q: 2. (Chapter 2, p.82) In computing Var(yoyo), where yo = Bo Bico and yo = Bo + Bixo + €0, we used…

A: The data given in the problem is as follows:It is required to express  as a linear combination of…

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: 5. Show that if m1, ..., mn are integers, then the number mj - mi j-i II 1<i<j≤n is an integer.…

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Q: then -A U= 4 5 and uTu · [

A: The given matrix

Q: 3.2.1 Example A Consider the three functions f1(k) = 3*, f2(k) = 3k+2, f3(k) = 2*, (3.39) and form…

A: We have to solve given problem:

Q: a) Find ū - i b) Find w.u 1/2

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Q: Consider the set S = {2x² + 1, 2x – 4, 2x + x}. The set S spans P2. If t(a) — 6а? + 6х — 15 € Ра,…

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

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Q: Given u(x)= x +3 and v(x)= 9x – 4, find u v. O 9x² – 12 - O 9x² + 27x – 4 O 9x+ 23 x - 12 O 9x + 23…

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Q: Use with (8'e) (-2,) (7,1)

A: Given query is to find indicated vector operation.

Q: Consider an unfair coin with probability p of heads. n has been tossed (a deterministic number) n…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: select the description that characterizes the Boolean expression

A: A boolean expression is CNF (Conjunctive normal form) if it is a product of sums. And, a boolean…

Q: Use the rules of inference to show that if Vx((A(x) → C(x)) v (B(x) → C(x))), 3x(A(x) V B(x)) and…

A: We have to prove , by using the rules of inference and applying universal instantiation,…

Q: Let a : V → W be a linear map for vector spaces V, W over R, V₁, V2, V3, V4 a basis of V and w₁, W2,…

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Q: = Let p(x) = x³ x² + 2x + 3, q(x) = 3x³ + x² − x − 1, r(x) = x³ + 2x + 2, and s(x) = 7x³ + ax² +5.…

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Q: Show that if AB={0}, then P(A)≤P(B).

A: Given that

Q: Which of the following statements is correct? a) P(X | Y) = P (X) if X and Y are independent.

A: Our aim is to find the correct statement.