is asking for the R code to set up things for 4b. There is no output...

 

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is asking for the R code to set up things for 4b. There is no output as such for (a). Here is an outline to set up the function. MCsim<-function(nsim, lambda) { cov1<-cov2<-rep(NA,nsim) # create empty matrices to store data for (i in 1:nsim) { x=rpois (...) # The question says Poisson xbar=............... #find mean of x Xsd=..... ..# find sd of x C11<-use the formula for conf interval for mean given in the question C12<-use the formula for conf interval for variance given in the question cov1 [i]<-(C11[1]<lambda) & (lambda<C11[2]) cov2[i]<-Do similarly using C12 } print (paste("When lambda=", lambda, ": coverage for first Cl is", mean(cov1), ", coverage for second Cl is", mean(cov2), ".")) # Just to keep your output presentable } Now use the function from 4(a) with your values of nsim and lambda and get the outputs. Remember the question is asking for 3 values of lambda. For example if you do MCsim(nsim=1000, lambda=0.5), you will get the output for lambda=0.5 and so on. For a random sample of 50 observations from Poisson we have two ways to construct a 90% CI for the parameter 2. distribution, (1) Since the Poisson mean is λ, we can use the interval for the sample mean . (2) Since the Poisson variance is also λ, we can use the interval for the sample variance directly: . (a) Write a R-script to conduct a Monte Carlo study for the coverage probabilities of the two CIs. That is, to generate nsim=1000 such data sets from the Poisson distribution. Check the proportion of the CIs that contains the true parameter 2. (b) Run the Monte Carlo simulation for nsim-1000 runs, at three different parameter values: λ=0.1, λ=1 and λ=10. Report the coverage probabilities of these two CIs at each of the three parameter values. (c) Considering your result in part (b), which one of these two CI formulas should you use in practice? Can you explain the pattern observed in (b)? is asking for the R code to set up things for 4b. There is no output as such for (a). Here is an outline to set up the function. MCsim<-function(nsim, lambda) { cov1<-cov2<-rep(NA,nsim) # create empty matrices to store data for (i in 1:nsim) { x=rpois (...) # The question says Poisson xbar=............... #find mean of x Xsd=..... ..# find sd of x C11<-use the formula for conf interval for mean given in the question C12<-use the formula for conf interval for variance given in the question cov1 [i]<-(C11[1]<lambda) & (lambda<C11[2]) cov2[i]<-Do similarly using C12 } print (paste("When lambda=", lambda, ": coverage for first Cl is", mean(cov1), ", coverage for second Cl is", mean(cov2), ".")) # Just to keep your output presentable } Now use the function from 4(a) with your values of nsim and lambda and get the outputs. Remember the question is asking for 3 values of lambda. For example if you do MCsim(nsim=1000, lambda=0.5), you will get the output for lambda=0.5 and so on. For a random sample of 50 observations from Poisson we have two ways to construct a 90% CI for the parameter 2. distribution, (1) Since the Poisson mean is λ, we can use the interval for the sample mean . (2) Since the Poisson variance is also λ, we can use the interval for the sample variance directly: . (a) Write a R-script to conduct a Monte Carlo study for the coverage probabilities of the two CIs. That is, to generate nsim=1000 such data sets from the Poisson distribution. Check the proportion of the CIs that contains the true parameter 2. (b) Run the Monte Carlo simulation for nsim-1000 runs, at three different parameter values: λ=0.1, λ=1 and λ=10. Report the coverage probabilities of these two CIs at each of the three parameter values. (c) Considering your result in part (b), which one of these two CI formulas should you use in practice? Can you explain the pattern observed in (b)?

Answer rating: 100% (QA)

a Sure heres an Rscript that c... View the full answer