Statement: Additive property of Poisson distribution states that sum of independent Poisson variates is also a Poisson variate. i.e., If X,,X,,. ., X, are n independent Poisson variates with parameters 4,2.. ., 2, respectively, then in EX, is also a Poisson variate with parameter E1, :

Q: (c) lim sup (an + bn) lim inf an + lim inf bn

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Q: Prove the following fact: A" = 3"-1A. 1 1 1 1 1 1 1 1 1 A =

A: Given, A =111111111  We have to  prove An = 3n-1A

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Q: f A is an event in the finite sample space, then prove that P (A) equals the sum of the…

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Q: friove it with atleant one one esuanple thein aLccb

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Q: Let A be an n x n matrix with eigenvalues A₁ and A2, where A₁ A2. If Sx, is the eigenspace…

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Q: 5n² is O(n³)

A: Suppose fn and gn are positive functions. We say that fn∈Ogn if there exist positive constants c, n0…

Q: Prove that for every integer n > 2, P(n+1, 3) = n³ . %3D -n.

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Q: 1 Show that (tan-' x) : 1+x?

A: We use Trigonometry identities and inverse Trigonometry to solve this proof

Q: Defn "x→x*lim Xj =x' 'x; "the limit of x; is x" convenges to * " Hl proue lim 5j-l %3D

A: To understand my solution, You first go through the definition of the limit. Then you must study…

Q: a) (A u B) = A N B b) (ANB) = A u B

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Q: Theorem 3-5. If B cA, then (i) P(AnB ) = P(A) – P(B), (ii) P(B)<P(A)

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Q: Compute the following. (a) P6, 2- (b) C6, 21 (c) Pa, s (d) Cg 9

A: The formula for Pn, r Pn, r  =n!n-r! The formula for Cn, r Cn, r  =n!r!×n-r! Here,  n!…

Q: Proposition 4.1.2. If ƒ : A → Rn satisfies the lower-Lipschitz condition on E, i.e., if there exists…

A: We will prove all by using the definitions

Q: (a) Let n be any integer. Prove that n2 is congruent to 0, 1 or 4 modulo 8.

A: Note: According to bartleby guidelines we have to answer only first question please upload the…

Q: L[y''''] L[f"'''']

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Q: Let p(x) and q(x) be predicates with variable x. Prove the following. • (3x)p(x) (x)~p(x) I(p q) =…

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Q: Prove that A2=I.

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Q: 8) Suppose A E Mnxn(F) is diagonalizable. Let A1,· , Ak be the (distinct) eigenvalues of A. a) Prove…

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Q: C. The Fibonacci numbers (Fn)n21 are defined by the recurrence F₁ = 1, F2 = 1, Fn = Fn-1 + Fn-2 for…

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Q: vx (P(x) → (Q(x) v R(x))), – 3x (P(x) ^ R(x)) | vx (P(x) → Q(x))

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Q: Let S= {n | n=5 k+ 4 for some integer k} Let T= {n|n=5 j– 1 for some integer j}

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Q: 29. For any odd integer n, n° n² +3 %3D 4 4

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Q: Let a 20 be a real number (to be chosen below) and recursively define an-1 + a2-1 an = 3 for n > 2.…

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Q: Prove the shown?

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Q: (BOC)=(A-B)u(A-C). 11. If A and B are sets in a universal set U, then AUB=AnB. 12. If A, B and C are…

A: To prove the equality A - (B ∩ C) = (A - B) ∪ (A - C), we need to show that each set is a subset of…

Q: (А - B) - С - (А -C)- (В - C)

A: Introduction :

Q: VII. Prove the following statements. 1. Let B be an orthonormal basis of a finite-dimensional inner…

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Q: (7) Let p be a prime number. Ihe there exists a positive real number x such that x= p. (8) Let S be…

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Q: An integer x is odd if x2 is odd. Let x, y and z be integers. If x y and y z, then x | z. For any…

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Q: (b) Prove that E-o(-1)* )= 0 for all positive integers m.

A: We have to prove ∑k=0n-1kkn=0 for all positive integer n