(b) Combining the result of the previous question with the Law of Large Numbers, show that the estimated probability of falling in bin i, as given by the histogram method, tends to fv, f(x)dx, the true probability of falling in bin i, as n→ ∞. Vi denotes the volume occupied by bin i.
(b) Combining the result of the previous question with the Law of Large Numbers, show that the estimated probability of falling in bin i, as given by the histogram method, tends to fv, f(x)dx, the true probability of falling in bin i, as n→ ∞. Vi denotes the volume occupied by bin i.
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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Solution for quetion (b) is needed
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![Consider a dataset {r;}"-1 where each point r E [0, 1]d. Let f(x) be
the true unknown data distribution. You decide to use a histogram
method to estimate the density f(x) and divide each dimension into
m bins.
(a) Show that for a measurable set S, E[1{resy] = P(r E S).
(b) Combining the result of the previous question with the Law of
Large Numbers, show that the estimated probability of falling in
bin i, as given by the histogram method, tends to fv. f(x)dx, the
true probability of falling in bin i, as n → o. V; denotes the
volume occupied by bin i.
4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43c7ed24-8834-4a07-8437-e66dda2ff35c%2Ffd38c8ee-1f16-4677-a1a7-cbe28a2ea933%2Fn6dbmia_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a dataset {r;}"-1 where each point r E [0, 1]d. Let f(x) be
the true unknown data distribution. You decide to use a histogram
method to estimate the density f(x) and divide each dimension into
m bins.
(a) Show that for a measurable set S, E[1{resy] = P(r E S).
(b) Combining the result of the previous question with the Law of
Large Numbers, show that the estimated probability of falling in
bin i, as given by the histogram method, tends to fv. f(x)dx, the
true probability of falling in bin i, as n → o. V; denotes the
volume occupied by bin i.
4
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