Program plan: String types variable lineOne, lineTwo, and lineThree stores the three strings provided. The standard output operator cout is used to print the permutation of these three statements. Program description: The purpose of this program is to print three lines of prose in all six possible orders of arrangement. This will be achieved by using a separate variable for each line and thereafter, changing the order of the lines in each iteration.

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?

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Chapter 2, Problem 2PP

Program Plan Intro

Program plan:

String types variable lineOne, lineTwo, and lineThree stores the three strings provided.

The standard output operator cout is used to print the permutation of these three statements.

Program description:

The purpose of this program is to print three lines of prose in all six possible orders of arrangement. This will be achieved by using a separate variable for each line and thereafter, changing the order of the lines in each iteration.

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