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d. Note that the probability of this data sample would be greater if the value of p(x = 1) was not 0.5, but instead some other value. What is the value that maximizes the probability of the sample S. Please justify your answer.

d. Note that the probability of this data sample would be greater if the value of p(x = 1) was not 0.5, but instead some other value. What is the value that maximizes the probability of the sample S. Please justify your answer.

MATLAB: An Introduction with Applications
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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Consider a sample of data S = {1, 1, 0, 1, 0} created by flipping a coin x five times, where 0 denotes that the coin turned up heads and 1 denotes that it turned up tails. a. What is the sample mean for this data? b. What is the sample variance for this data? c. What is the probability of observing this data, assuming it was generated by flipping a coin with an equal probability of heads and tails (i.e. the probability distribution is p(x = 1) = 0.5, p(x = 0) = 0.5). d. Note that the probability of this data sample would be greater if the value of p(x = 1) was not 0.5, but instead some other value. What is the value that maximizes the probability of the sample S. Please justify your answer.
Transcribed Image Text:Consider a sample of data S = {1, 1, 0, 1, 0} created by flipping a coin x five times, where 0 denotes that the coin turned up heads and 1 denotes that it turned up tails. a. What is the sample mean for this data? b. What is the sample variance for this data? c. What is the probability of observing this data, assuming it was generated by flipping a coin with an equal probability of heads and tails (i.e. the probability distribution is p(x = 1) = 0.5, p(x = 0) = 0.5). d. Note that the probability of this data sample would be greater if the value of p(x = 1) was not 0.5, but instead some other value. What is the value that maximizes the probability of the sample S. Please justify your answer.
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