Homework 6 in STAT400: Computational Statistics @ CSU
Be sure to set.seed(400)
at the beginning of your
homework.
Develop two Monte Carlo integration approaches to estimate \(\int\limits_0^5 x^2 \exp(-x) dx\). (You
must use different distributions in the two approaches). Check your
answer using the integrate()
function.
Estimating the cdf of a normal distribution. Use \(m = 1000\).
R
function pnorm()
for \(x = 0.5,
1, 2, 3\). Summarise your findings comparing the performance of
the methods.Compute a Monte Carlo estimate \(\hat{\theta}_1\) of \[ \theta = \int\limits_0^{0.5} e^{-x} dx \] by sampling from the Uniform(\(0, 0.5\)) and estimate the variance of \(\hat{\theta}_1\). Find another Monte Carlo estimator \(\hat{\theta}_2\) by sampling from the Exponential(1) distribution and estimating its variance.
Which of the variances (of \(\hat{\theta}_1\) or \(\hat{\theta}_2\)) is smaller?
Turn in in a pdf of your homework to canvas. Your .Rmd file on the server will also be used in grading, so be sure they are identical and reproducible.
Be sure to share your server project with the instructor and grader:
Open your hw-6 project on liberator.stat.colostate.edu
Click the drop down on the project (top right side) > Share Project…
Click the drop down and add “stat400instructors” to your project.
This is how you receive points for reproducibility on your homework!