2. Show that the maximum likelihood estimate for P(wi) is P(w) = Zik %3D k31 Interpret your result in words.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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Problem 3
Maximum likelihood methods apply to estimates of prior probabilities as well. Let samples
be drawn by successive, independent selections of a state of nature w with unknown
probability P(@). Let zr = 1 if the state of nature for the kth sample is w; and zik = 0
otherwise.
1. Show that
2. Show that the maximum likelihood estimate for P(wi) is
P(w)
Zik
k=1
Interpret your result in words.
Transcribed Image Text:Problem 3 Maximum likelihood methods apply to estimates of prior probabilities as well. Let samples be drawn by successive, independent selections of a state of nature w with unknown probability P(@). Let zr = 1 if the state of nature for the kth sample is w; and zik = 0 otherwise. 1. Show that 2. Show that the maximum likelihood estimate for P(wi) is P(w) Zik k=1 Interpret your result in words.
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