Introduction to Probability · Problem 8.1.7

Law of Large Numbers — Grinstead & Snell

Mathematics — Probability · chebyshev-inequality-bernoulli

Problem

Find the maximum possible value for p(1−p)p(1-p) if 0<p<10 < p < 1. Using this result and Exercise 6, show that the estimate P(∣Snn−p∣≥ϵ)≤14nϵ2P\left(\left|\frac{S_n}{n} - p\right| \geq \epsilon\right) \leq \frac{1}{4n\epsilon^2} is valid for any pp.

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