In order to estimate the probability of an event A, a sequence of n Bernoulli trials is carried out and the relative frequency of A is observed. How large should n be in order to have a 0.8 probability that the relative frequency is within 0.08 of p = P[A]? Hint: Use the Chebyshev inequality: for all e > 0, P[|X - E[X]>=e] <= Var[X]/e²; and the fact that p(1-p) is at most 1/4 for p in [0,1]. 196.00 232.00 144.00 179.00
In order to estimate the probability of an event A, a sequence of n Bernoulli trials is carried out and the relative frequency of A is observed. How large should n be in order to have a 0.8 probability that the relative frequency is within 0.08 of p = P[A]? Hint: Use the Chebyshev inequality: for all e > 0, P[|X - E[X]>=e] <= Var[X]/e²; and the fact that p(1-p) is at most 1/4 for p in [0,1]. 196.00 232.00 144.00 179.00
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![In order to estimate the probability of an event A, a sequence of n Bernoulli trials is carried out and the relative frequency of A is observed. How large should n be in order to have a 0.8 probability
that the relative frequency is within 0.08 of p = P[A]?
Hint: Use the Chebyshev inequality: for all e > 0, P[|X - E[X]>=e] <= Var[X]/e²; and the fact that p(1-p) is at most 1/4 for p in [0,1].
196.00
232.00
144.00
179.00](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6d84cec-6eea-48fe-beab-f57f8d5ced4f%2F4b536f31-1085-4865-acf3-479d3e2d35ea%2Fcricro_processed.png&w=3840&q=75)
Transcribed Image Text:In order to estimate the probability of an event A, a sequence of n Bernoulli trials is carried out and the relative frequency of A is observed. How large should n be in order to have a 0.8 probability
that the relative frequency is within 0.08 of p = P[A]?
Hint: Use the Chebyshev inequality: for all e > 0, P[|X - E[X]>=e] <= Var[X]/e²; and the fact that p(1-p) is at most 1/4 for p in [0,1].
196.00
232.00
144.00
179.00
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