Consider flipping a (biased) coin for which the probability of head is p. The fraction of heads after n independent tosses is Xn. Law of large numbers imply that X, p as n → 0o. This does not mean...

$Consider flipping a (biased) coin for which the probability of head is p. The fraction of heads after n independent tosses is Xn. Law of large numbers imply that X, p as n → 0o. This does not mean that X, will exactly equal to p, but rather the distribution of X is tightly concentrated around p for large n. (a) Suppose 0.1 <p<0.9. Use Chebyshev's inequality to obtain a lower bound on P(p – 0.1 < X, <p+ 0.1). $

Extracted text: Consider flipping a (biased) coin for which the probability of head is p. The fraction of heads after n independent tosses is Xn. Law of large numbers imply that X, p as n → 0o. This does not mean that X, will exactly equal to p, but rather the distribution of X is tightly concentrated around p for large n. (a) Suppose 0.1

Jun 11, 2022

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Consider flipping a (biased) coin for which the probability of head is p. The fraction of heads after n independent tosses is Xn. Law of large numbers imply that X, p as n → 0o. This does not mean...

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