Assignments

Homework01: (due Wednesday Sept. 3)

Your handwritten homework solutions should be submitted through Canvas. Your papers should be scanned in the order assigned. Your name should appear on each page. I would suggest starting each problem at the top of a new page so it is clear which problem you are working on.

Your R code should be completed in an R Quarto Notebook Rendered to a .html file and submitted through Canvas, submit both the .qmd file and the .html file. The YAML header of your R Quarto Notebook should look like the following (with your name and the date you submit the assignment):

---
title: "Stat. 640 Homework 1"
author: "Your name"
date: "August 25, 2025"
format:
  html:
    embed-resources: true
---

Exercise 1: Use R to

  1. Plot the model BIN(\(n\) = 10, \(p\) = 0.5)
  2. Plot the model POIS(\(\lambda\) = 5)
  3. Determine the value of the 25th percentile (quantile) for each distribution.

Exercise 2: Using R simulate \(n\) = 100 standard normal values, square each value, and plot histograms. Comment on the shape of the distribution.

Exercise 3:

  1. Using R plot the model Exponential p.d.f. for \(\lambda\) = 0.4, 1, 8. Determine the 25th percentile (quantile) for each distribution.
  2. Using R plot the model Gamma p.d.f. for \(\alpha\) = 1, \(\lambda\) = 0.4, 1, 8 and for \(\alpha\) = 0.5, 1, 5, \(\lambda\) = 2.5. Determine the 25th percentile (quantile) for each distribution.