# Integrals simulation in the program R

by Sajjad Esmaili   Last Updated May 16, 2019 06:19 AM

let $$x|\lambda \sim exp (\lambda) \to \lambda | x \sim \Gamma(2,x)$$ , $$L(\theta , a)=(\theta-a)^2$$ , $$\theta=\lambda\to E^{\pi}(\theta)=2/\pi$$

if $$L(\theta -a)=|\theta-a|, p(theta \leq \sigma^{\pi}(x)|x)=1/2$$ not that $$f(\lambda | x) = x^2 \lambda e^{- \lambda x}$$ with a numberic appaocch find $$\sigma^{\pi}$$ shoche that $$\int_0^{\sigma^\pi (x)} x^2 \lambda e^{-\lambda x} d x =1/2$$ I want this integral to simulate

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