6. Generate a random variable X from the semicircular density 2 f(x) = πR2 √R²x², -R < x < R. Take the proposal distribution to be uniform over [-R, R], that is, take g(x) = 1/(2R) with -RxR and choose C as small as possible such that Cg(x) > f(x).
6. Generate a random variable X from the semicircular density 2 f(x) = πR2 √R²x², -R < x < R. Take the proposal distribution to be uniform over [-R, R], that is, take g(x) = 1/(2R) with -RxR and choose C as small as possible such that Cg(x) > f(x).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 20E
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(a) Show that C = 4/π.
(b) Construct the Neumann method, find the expected number of trials (per one acceptance), and find the computational cost (efficiency).
![6. Generate a random variable X from the semicircular density
2
f(x) =
=
-
R² – x², -R< x < R.
πR²
Take the proposal distribution to be uniform over [-R, R], that is, take g(x)
-R< x < R and choose C as small as possible such that Cg(x) > f(x).
=
1/(2R) with](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91f76606-a4d9-42f0-be0d-7b1366a5593f%2F8bbb484f-6d2f-43cf-a78a-639f07280b27%2F6cxli2r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. Generate a random variable X from the semicircular density
2
f(x) =
=
-
R² – x², -R< x < R.
πR²
Take the proposal distribution to be uniform over [-R, R], that is, take g(x)
-R< x < R and choose C as small as possible such that Cg(x) > f(x).
=
1/(2R) with
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