Physics $4730,$ Fall $2024$

Homework #$4$

Due Sunday November $3^{rd}$

Write a Python script

quantile.py which reads in an unknown random variable from a one$-$column file rvvec.dat and estimates the $$ quantile of the data and it's $95\%$ confidence interval using the empirical likelihood method. $$ should be passed to your script on the command line.

For example, if I call your script as follows:

belz@canis $>$ python$3$

quantile.py $0\mathrm{.}5$

then the script should read rvvec.dat $($assumed to be in the same directory as your script$),$ compute the median $(50\%$ of the data below this value of the RV$)$ and provide a range of the RV in which we can be $95\%$ certain the "true" median lies.

The $0\mathrm{.}500$ quantile of the data is: $x.$

The $95$ pct CI is $($y$.$yyyyyy$,$ z$.$zzzzzzz$)$

It is likely useful, but not required, that you produce a plot to confirm your calculation is doing something sensible$.$