The red part is the homework that needs to be done The red part is the homework that needs to be done Thanks a lot！！！
The red part is the homework that needs to be done The red part is the homework that needs to be done Thanks a lot！！！
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
The red part is the homework that needs to be done
The red part is the homework that needs to be done
Thanks a lot！！！
![& Practitioner's corner
Usually, the problem appears as follows: there exists a random variable E = L (N,
A, P) such that:
(i) E E can be computed at a very low cost by a deterministic method (closed
form, numerical analysis method),
(ii) the random variable X-E can be simulated with the same cost (complexity)
as X,
Ì) E[0] koun mit sehr geringem Aufwand durch ein deterministisches Verfuhren (geschlossene Form, numerisches Analysis vorfubrows
berechnet werden.
ii) die Zufallsvariable X- Ⓒ kann mit den gleichen kasten (komplexität) wie X simuliert worden.
111) Var (x-6) < Var (X)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0eba744-2ca5-4b9b-b356-631e195ec79e%2Fad421f31-e2f5-4db5-aac4-052b0303e823%2Fh1a58j_processed.png&w=3840&q=75)
Transcribed Image Text:& Practitioner's corner
Usually, the problem appears as follows: there exists a random variable E = L (N,
A, P) such that:
(i) E E can be computed at a very low cost by a deterministic method (closed
form, numerical analysis method),
(ii) the random variable X-E can be simulated with the same cost (complexity)
as X,
Ì) E[0] koun mit sehr geringem Aufwand durch ein deterministisches Verfuhren (geschlossene Form, numerisches Analysis vorfubrows
berechnet werden.
ii) die Zufallsvariable X- Ⓒ kann mit den gleichen kasten (komplexität) wie X simuliert worden.
111) Var (x-6) < Var (X)
![=)
3.1 The Monte Carlo Method Revisited: Static Control Variate
(iii) the variance Var (X - E) < Var(X).
Then, the random variable
EX-ECx- +0]]
[[X] -
can be simulated at the same cost as X,
Varcx)=VarcX-0+E(91)
X'= X-E + E3
51
EX'=EX = m and Var(X') = Var(X - E) < Var(X).
Definition 3.1 A random variable E satisfying (i)-(ii)–(iii) is called a control
variate for X.
► Exercise. Show that if the simulation process of X and X - E have complexity
K and K' respectively, then (iii) becomes
(iii)' K' Var (X - =) < ‹ Var(X).
The product of the variance of a random variable by its simulation complexity is
called the effort. It will be a central notion when we will introduce and analyze
Multilevel methods in Chap. 9.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0eba744-2ca5-4b9b-b356-631e195ec79e%2Fad421f31-e2f5-4db5-aac4-052b0303e823%2Firblk6o_processed.png&w=3840&q=75)
Transcribed Image Text:=)
3.1 The Monte Carlo Method Revisited: Static Control Variate
(iii) the variance Var (X - E) < Var(X).
Then, the random variable
EX-ECx- +0]]
[[X] -
can be simulated at the same cost as X,
Varcx)=VarcX-0+E(91)
X'= X-E + E3
51
EX'=EX = m and Var(X') = Var(X - E) < Var(X).
Definition 3.1 A random variable E satisfying (i)-(ii)–(iii) is called a control
variate for X.
► Exercise. Show that if the simulation process of X and X - E have complexity
K and K' respectively, then (iii) becomes
(iii)' K' Var (X - =) < ‹ Var(X).
The product of the variance of a random variable by its simulation complexity is
called the effort. It will be a central notion when we will introduce and analyze
Multilevel methods in Chap. 9.
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