29 (a) Prove that for all x 0, Hint Integrate the following inequalities (b) Use part (a) to prove that 1 (x) 1 x2 ex2 2 That is, as x , the ratio of the two sides approaches 1 1 x2 1 (x) (x) 1 (1) 1 22 12 2...

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29. (a) Prove that for all x > 0, Hint: Integrate the following inequalities (b) Use part...

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29.

(a) Prove that for all x > 0,

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Hint: Integrate the following inequalities

(b) Use part

(a) to prove that 1 − (x) ∼
1 x√2π
e−x2/2. That is, as x → ∞, the ratio of the two sides approaches 1.

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Fundamentals Of Probability With Stochastic Processes

ISBN: 9780429856273

4th Edition

Authors: Saeed Ghahramani

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Question Posted: Nov 18, 2024 12:00 AM

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29. (a) Prove that for all x > 0, Hint: Integrate the following inequalities (b) Use part...

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1 x2 <1-(x) < (x) 1> -(1) 1 22 -12/2

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Fundamentals Of Probability With Stochastic Processes

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