2. Recall the Poisson changepoint example from section 9.5 of the textbook. The dataset records the number of coal mine explosions that resulted in 10 or more fatalities each year from March 15, 1851 to March 22,1962. It appears that after a certain point, the rate of disasters decreased. Let Y, be the number of disasters in year i, where 1851 is year 1. Assume Yi ~ Poisson(u) for i = 1, 2, ..., k Yi ~ Poisson()) for i = k + 1, ...,n. The likelihood function is L(k, p, x) = (II yi! -)II ya! i=1 i=k+1 Compute the maximum likelihood estimate of the parameter vector (k, /, A). To get the data in the shape you need, run the following code. library (boot) y=floor (coal [ [1]]) y=tabulate(y) y y [1851 : length(y) ]