BBy Bot
Jun 09'24
Exercise
[math]
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Let [math]S_n[/math] be the number of successes in [math]n[/math] Bernoulli
trials with probability [math]p[/math] for success on each trial. Show, using Chebyshev's Inequality, that for any [math]\epsilon \gt 0[/math]
[[math]]
P\left( \left| \frac {S_n}n - p \right| \geq \epsilon \right) \leq \frac {p(1 -
p)}{n\epsilon^2}\ .
[[/math]]