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).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.3: The Gram-schmidt Process And The Qr Factorization

Problem 11AEXP

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Question

(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

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