ssume X ∼ Poisson(r), where r > 0. Prove that E(X) = r.

Q: (13) Prove by induction that for each whole number n, 1. You may use the fact that for each whole…

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Q: x+y uis = 1 n upi = no • prove that x-+ y-

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Q: Let X Gamma(a, B). Prove that for any positive integer n > 1, E(X") = [(a +n– 1)(a+n – 2)..-a]3".

A: It is given in the question that X~Gammaα,β then we have to prove that for any positive integer n≥1.…

Q: 1 Prove that 3 dx s VI VI

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Q: Prove using the IVT cosx = cos-1x has a solution in (0, 1).

A: cos x = x   rearrange to x - cos x = 0

Q: Use mathematical induction to prove that cos(x+n) = (-1)" cosx where n≥le J*.

A: Mathematical induction is defined as a mathematical technique that is used for the expression,…

Q: Use Cauchy to integrate the following T ez - e-z 24 dz

A: The integral  is :The main to evaluate the integral using the Cauchy formula

Q: Solve using the false rule method f(x) = /x² + 1 – tan x %3D starting at the interval [0.5,1]

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Q: Prove the following identity: (x + y)2- (x-y)? = 4xy %3D

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Q: ) Prove that sac"()/T sec

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Q: Let f(x) = 3 cos 2x + sin² x. a) b) Show that f'(x) = -5 sin 2x. Зл In the interval <x< one normal…

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