Consider a dataset {x}=1 where each point x = [0, 1]ª. 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[1reS}] = P(x € S).
Consider a dataset {x}=1 where each point x = [0, 1]ª. 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[1reS}] = P(x € S).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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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%2Fa9796537-9cd3-4b5b-a2bc-95d9fdbe71c5%2Frgp1ral_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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