题目
题目

25F-STATS-102C-LEC-1 Quiz3- Requires Respondus LockDown Browser

单项选择题

Let 𝑓 ( 𝑥 ) = 𝑐 𝑜 𝑠 ( 𝑥 ) , for 𝑥 ∈ [ 0 , 𝜋 / 2 ] . Suppose we want to sample 𝑓 ( 𝑥 ) through the rejection method, with 𝑈 𝑛 𝑖 𝑓 ( 0 , 𝜋 / 2 )  as the candidate density. What is the multiplicative constant M?

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标准答案
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思路分析
We’re sampling from a target density proportional to f(x) = c cos x on the interval [0, π/2] using a candidate density g(x) that is Uniform on [0, π/2]. First, identify the densities: the uniform candidate has density g(x) = 1 / (π/2) = 2/π for x in [......Login to view full explanation

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类似问题

Consider the probability function as follows. We want to generate random samples from p(x) through the rejection method.    x 0 1 2 p(x) 1/3 2/5 4/15   Suppose we have two candidate probability functions: (1)  x 0 1 2 g1(x) 1/3 1/3 1/3 (2) x 0 1 2 g2(x) 1/2 1/4 1/4   Which candidate probability function is more efficient in the best-case scenario?

Let 𝑓 ( 𝑥 ) = 𝑠 𝑖 𝑛 ( 𝑥 ) , for 𝑥 ∈ [ 0 , 𝜋 / 2 ] . Would the following R code generate the random samples of f(x)? m <- 1000 u <- runif(m) x <- u * pi / 2-----------------------------------------------------(1) M <- max(sin(x) / (2 / pi))---------------------------------------(2) x_accepted <- x[which(u <= sin(x) / (M * (2 / pi)))] ----------(3)  

Considering the rejection method algorithm, all the required conditions are satisfied with the candidate density 𝑔 ( 𝑥 ) and multiplicative constant M,  what is the range of 𝑓 ( 𝑥 ) 𝑀 𝑔 ( 𝑥 ) ?

Consider the probability function as follows. We want to generate random samples from p(x) through the rejection method. Suppose we use the discrete uniform as our g(x). Here we set g(0) = 0.4, g(1) =0.4, and g(2)=0.2. Please approximate the acceptance rate and select the closest value from the options below.   x 0 1 2 p(x) 1/3 2/5 4/15    

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