The red part is the homework that needs to be doneThe red part is the homework that needs to be doneThanks a lot！！！ & Practitioner's cornerUsually, 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 (closedform, 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 vorfubrowsberechnet 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 variableEX-ECx- +0]][[X] -can be simulated at the same cost as X,Varcx)=VarcX-0+E(91)X'= X-E + E351EX'=EX = m and Var(X') = Var(X - E) < Var(X).Definition 3.1 A random variable E satisfying (i)-(ii)–(iii) is called a controlvariate for X.► Exercise. Show that if the simulation process of X and X - E have complexityK 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 iscalled the effort. It will be a central notion when we will introduce and analyzeMultilevel methods in Chap. 9.

To show that if the simulation process of X and X - E have complexity K and K' respectively, then…

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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！！！

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...

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Question

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)

=)
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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