Given a coin with the probability p of landing heads, where p is unknown and we need to estimate its value through data. In our data collection model, we have n independent tosses, result of each toss is either Head or Tail. Let X denote the number of heads in the total n tosses. Now we conduct experiments to collect data and find out that X = k. Then we need to find . the estimation of p. (a) Assume p is an unknown constant. Find through the MLE (Maximum Like- lihood Estimation) rule. (b) Assume Р is a random variable with a prior distribution Beta(a, b), where a and b are known constants. Find p through the MAP (Maximum a Posterior Probability) rule (c) Assume p is a random variable with a prior distribution Beta(a, b), where a and b are known constants. Find p through the MMSE (Minimum Mean Square Estimate) rule. 2 19 H SR #
Given a coin with the probability p of landing heads, where p is unknown and we need to estimate its value through data. In our data collection model, we have n independent tosses, result of each toss is either Head or Tail. Let X denote the number of heads in the total n tosses. Now we conduct experiments to collect data and find out that X = k. Then we need to find . the estimation of p. (a) Assume p is an unknown constant. Find through the MLE (Maximum Like- lihood Estimation) rule. (b) Assume Р is a random variable with a prior distribution Beta(a, b), where a and b are known constants. Find p through the MAP (Maximum a Posterior Probability) rule (c) Assume p is a random variable with a prior distribution Beta(a, b), where a and b are known constants. Find p through the MMSE (Minimum Mean Square Estimate) rule. 2 19 H SR #
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Given a coin with the probability p of landing heads, where p is unknown and we
need to estimate its value through data. In our data collection model, we have n independent
tosses, result of each toss is either Head or Tail. Let X denote the number of heads in the total
n tosses. Now we conduct experiments to collect data and find out that X = k. Then we need
to find . the estimation of p.
(a)
Assume p is an unknown constant. Find through the MLE (Maximum Like-
lihood Estimation) rule.
(b)
Assume Р is a random variable with a prior distribution Beta(a, b), where a
and b are known constants. Find p through the MAP (Maximum a Posterior Probability)
rule
(c)
Assume p is a random variable with a prior distribution Beta(a, b), where a and
b are known constants. Find p through the MMSE (Minimum Mean Square Estimate) rule.
2
19
H
SR
#
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