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Chapter 19.1, Problem 19.4CP

What STL types does the STL stack container adapt?

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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?
using r language A continuous random variable X has density function f(x)=1/56(3x^2+4x^3+5x^4).0<=x<=2 (1) secify the density g of the random variable Y you find for the acceptance rejection method. (2) what is the value of c you choose to use for the acceptance rejection method (3) use the acceptance rejection method to generate a random sample of size 1000 from the distribution of X .graph the density histogram of the sample and compare it with the density function f(x)
using r language a continuous random variable X has density function f(x)=1/4x^3e^-(pi/2)^4,x>=0  derive the probability inverse transformation F^(-1)x where F(x) is the cdf of the random variable X

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