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2. Let X₂'s be i.i.d. random variables where each X, is 1 with probability 1/2 ₁ X₁ and μ = n/2. In class, we showed the proof of the =1 and 0 otherwise. Let X = = following Pr[X > (1+8)µ] ≤e-¹(8²μ) е Show that the following inequality also holds. e-(8²μ) Pr[X < (16)μ] ≤ e²

2. Let X₂'s be i.i.d. random variables where each X, is 1 with probability 1/2 ₁ X₁ and μ = n/2. In class, we showed the proof of the =1 and 0 otherwise. Let X = = following Pr[X > (1+8)µ] ≤e-¹(8²μ) е Show that the following inequality also holds. e-(8²μ) Pr[X < (16)μ] ≤ e²

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!
2. Let X;'s be i.i.d. random variables where each X, is 1 with probability 1/2 and 0 otherwise. Let X = Σ₁ X; and µ = n/2. In class, we showed the proof of the following Pr[X > (1 + 6)µ] ≤ e−N(8²µ) Show that the following inequality also holds. Pr[X < (1 − 6)µ] ≤ e−¹(8²µ)
Transcribed Image Text:2. Let X;'s be i.i.d. random variables where each X, is 1 with probability 1/2 and 0 otherwise. Let X = Σ₁ X; and µ = n/2. In class, we showed the proof of the following Pr[X > (1 + 6)µ] ≤ e−N(8²µ) Show that the following inequality also holds. Pr[X < (1 − 6)µ] ≤ e−¹(8²µ)
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