# homework #1

The objectives of this homework assignment are the followings:

• Build your own RMarkdown document.
• Master different aspects of RMarkdown syntax.
• Become familiar with GitHub as a collaborative tool.

This homework must be accomplished using GitHub and respect the following requirements:

• All members of the group must commit at least once.
• All commit messages must be reasonably clear and meaningful.
• Your GitHub repository must include at least one issue containing some form of TO DO list.

In your repository, create a RMarkdown file called hw1.Rmd providing an HTML output with the theme cerulean and syntax highlighting tango. This file should contain the following elements:

• A “title” section which should at least include:
• A title (e.g. Homework 1)
• The authors
• The date (think of using Sys.time())
• A section called “Introduction” where you provide a short summary of the structure of your homework. Moreover, record a short video to introduce your group and include it in your RMarkdown document.
• A section called “Group Members”. This section should have one sub-section for each group member in your team. For example, a group with three members should have three sub-sections. Each of these sub-sections (named after each group member) should include small biographies containing at least the following elements:
• A picture of your choice. Make sure to include a caption for this image.
• A paragraph describing your favorite hobby as well as one interesting fact about yourself (preferably true).
• Your favorite quote in blockquote format. Make sure to reference your quote using BibTex.
• A table having two columns (first column containing the classes you are following this semester; second column containing the time of these classes).
• A section called “RMarkdown Syntax”, where you will demonstrate your RMarkdown skills! In this section make sure to:
• Show an example where the chunk option cache = T leads to a misleading answer. This example must be different from the one presented in the textbook.
• Simulate 300 random samples from a distribution that is uniform on [-1, 1] interval using the function runif(). Store these 300 values in a vector called x. Then, compute the empirical median, mean and variance of x. Are these results different from 0, 0 and 13 (their respective theoretical values)? Is this result surprising? Justify your answer.
• Include a graph showing the density estimation of x (make sure to include a caption to this figure). You can use the R function d <- denstiy() with default parameters, and the plot(d) function. Why does the estimated density exceed the [-1, 1] interval?
• Include the following equation:
• Include the following in-line equation:
• Include the following text in green: “The degree of civilization in a society can be judged by entering its prisons.”, Fyodor Dostoevsky