readme: add exercises 2,3

README.md

@@ -3,9 +3,9 @@
 
 ## Description
 
-This repository contains source code of two documents
+This repository contains the source code of two documents
 
-- `lectures`: an summary of the lectures of the course
+- `lectures`: a summary of the lectures of the course
 
 - `notes`: an explanation of the solutions of the exercises
 
@@ -69,8 +69,47 @@ different samples by changing the seed via the environment variable
 
 `ex-1/bin/main` generate random numbers following the Landau distribution and
 run a series of test to check if they really belong to such a distribution.  
-
 The size of the sample can be controlled with the argument `-n N`.  
-
 The program outputs the result of a Kolmogorov-Smirnov test and t-tests
 comparing the sample mode, FWHM and median, in this order.
+
+`ex-1/bin.pdf` prints a list of x-y points of the Landau PDF to the `stdout`.
+The output can be redirected to `ex-1/pdf-plot.py` to generate a plot.
+
+
+### Exercise 2
+
+Every program in `ex-2` computes the best available approximation (with a given
+method) to the Euler-Mascheroni γ constant and prints[1]:
+
+1. the leading decimal digits of the approximate value found
+
+2. the exact decimal digits of γ
+
+3. the absolute difference between the 1. and 2.
+
+[1]: Some program may also print additional debugging information.
+
+`ex-2/bin/fancy`, `ex-2/bin/fancier` can compute γ to a variable precision and
+take therefore the required number of decimal places as their only argument.
+The exact γ digits (used in comparison) are limited to 50 and 500 places,
+respectively.
+
+
+### Exercise 3
+
+`ex-3/bin/main` generates a sample of particle decay events and attempts to
+recover the distribution parameters via both a MLE and a χ² method. In both
+cases the best fit and the parameter covariance matrix are printed.  
+The program then performs a t-test to assert the compatibility of the data with
+two hypothesis and print the results in a table.
+
+To plot a 2D histogram of the generated sample do
+
+    $ ex-3/bin/main -i | ex-3/plot.py
+
+In addition the program accepts a few more parameters to control the histogram
+and number of events, run it with `-h` to see their usage.
+
+Note: the histogram parameters affect the computation of the χ² and the
+relative parameter estimation.