Operating System (OS): The most important program that runs on a computer is operating system. OS is the term that acts as an interface between the hardware and the user. OS does basic operations such as getting input from the keyboard, displaying output in the monitor and monitoring the files. It is responsible for the management to co-ordinate the activities on a computer system. The responsibilities of OS are bound to get higher when it comes to security, because it provides the access rights for users. Windows: Windows is one of the operating systems that develop new versions frequently. It is an aggregation of operating systems developed by Microsoft. It includes Graphical User Interface (GUI) that helps in displaying the required data on the desktop or monitor. It includes various features like hardware adaptability and interdependence, memory management, task management, access security and many others.

Question

using r language for integration theta = integral 0 to infinity (x^4)*e^(-x^2)/2 dx (1) use the density function of standard normal distribution N(0,1) f(x) = 1/sqrt(2pi) * e^(-x^2)/2 -infinity <x<infinity as importance function and obtain an estimate theta 1 for theta set m=100 for the estimate whatt is the estimate theta 1? (2)use the density function of gamma (r=5 λ=1/2)distribution f(x)=λ^r/Γ(r) x^(r-1)e^(-λx) x>=0 as importance function and obtain an estimate theta 2 for theta set m=1000 fir the estimate what is the estimate theta2? (3) use simulation (repeat 1000 times) to estimate the variance of the estimates theta1 and theta 2 which one has smaller variance?

Answer 1

Question

Chapter 9, Problem 41SG

Program Plan Intro

Operating System (OS):

The most important program that runs on a computer is operating system.

OS is the term that acts as an interface between the hardware and the user.

OS does basic operations such as getting input from the keyboard, displaying output in the monitor and monitoring the files.

It is responsible for the management to co-ordinate the activities on a computer system.

The responsibilities of OS are bound to get higher when it comes to security, because it provides the access rights for users.

Windows:

Windows is one of the operating systems that develop new versions frequently.

It is an aggregation of operating systems developed by Microsoft.

It includes Graphical User Interface (GUI) that helps in displaying the required data on the desktop or monitor.

It includes various features like hardware adaptability and interdependence, memory management, task management, access security and many others.

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