Now, let's approach the same data as Problem $2$ using the maximum likelihood method.

You should create a Python script

muon$-$maxl.py to perform the following:

Open the data file and store the unbinned decay times.

$($Note that, in your function that calculates log likelihood, you have to be a little

careful to make sure that your PDF is normalized to unity.$)$

For values of the parameter $$ in the range microseconds, with

step sizes $=0\mathrm{.}01$ microseconds, compute the log$-$likelihood. Make a plot of

$log-$likelihood versus $,$ and find the best$-$fit value of $.$ Find the uncertainty in $$

by finding the values ${}_{-}$and ${}_{+}$at which the log$-$likelihood decreases by $\frac{1}{2}($an

absolute number, not fractional change!$)$ relative to the maximum. Note that

your uncertainties may not be symmetric.

Print your results to standard output and create a final plot muon$-$maxl.png of

the data overlaid with your best fit.

Submit your Python script

muon$-$maxl.py$.$