MAT013 Coursework

Deadline: 2016/05/11

Instructions

The outputs of this coursework will be:

• A written report describing your code (SAS and R) to be handed in to Lauren Trundle.
• An appendix containing a commented version of your code (SAS and R) to be handed in to Lauren Trundle.
• A file containing the required SAS code. Name this file SAS-lastname-STUDENTNUMBER (eg. SAS-Knight-123456) and email it to Lauren Trundle with MAT013 as the subject. Note that all operations needed to complete the coursework should be included in the SAS code.
• A file containing the required R code. Name this file R-lastname-STUDENTNUMBER (eg. R-Knight-123456) and email it to Lauren Trundle with MAT013 as the subject. Note that all operations needed to complete the coursework should be included in the R code.

Coursework

1. Using both SAS and R (in other words attempt this question using SAS and then using R):

   Write code (in SAS: a macro, in R: a function) that will reproduce a mathematical procedure covered in MAT001 or MAT002. Clearly document this procedure in your report.

   [20]

2. Consider the data set two_thirds.csv which contains two columns of numerical data. These represent 1st and 2nd guesses for the game: “Two Thirds of the Average”.

   The rules of which are explained here: vknight.org/two_thirds_of_the_average_game/two_thirds_of_average_game_fill_in_sheet.pdf

   Using SAS:

   1. Draw two histograms: one for each set of guesses.
   2. Identify the winning guess for each set of guesses.

   Attempt to do this in a generic way (so that your code would work for a different data set).

   [25]

3. Consider the data set jokes.csv which contains jokes that have been ranked for the Edinburgh Fringe Festival for the years 2009-2015.

   Using R:

   1. Identify the effect of joke length on the performance of a joke.
   2. Identify if authors who have repeated entries seem to do better than authors who do not.

   (Note that this question is not asking for sophisticated sentiment analysis.)

   [25]

4. Using SAS or R:

   1. Write code that generates a random ‘stochastic matrix’ \(P\): a square matrix of size (\(N\)) with the following properties:

      $$\sum_{j=1}^{N}P_{ij}=1 \text{ for all }1\leq i\leq N$$

      and:

      $$P_{ij}\geq 0\text{ for all }1\leq i,j \leq N$$

      [15]

   2. Using the above, simulate a Stochastic process in which state \(i\) ‘moves’ to state \(j\) with probability given by \(P_{ij}\). Expected outputs include: the probability of being in each state.

      [15]

   3. Write a data set with 1000 different matrices \(P\) and the corresponding probability distribution.

      [10]