1. The file twoexondata.txt has 3000 pairs of (first, second) exon lengths. Choose 600 of the first exon lengths at random. Then, in your favorite programming language, repeat the calculation shown in the segment to model the chosen first exon lengths as a mixture of two Student distributions. That is (see slide 2): "6 parameters: two centers, two widths, ratio of peak heights, and Student t index." After running your Markov chain, plot the posterior distribution of the ratio of areas of the two Student components, as in slide 6.
2. Make a histogram of the 2nd exon lengths. Do they seem to require two separate components? If so, repeat the calculations of problem 1. If not, use MCMC to explore the posterior of a model with a single Student component. Plot the posterior distribution of the Student parameter ν.