The $()$ in the above integral is the probability density function of $.$ What you need to do here is to verify the above answer using Monte Carlo simulation. Find out how to make use of numpy.random.exponential to draw $10,000,000$ samples of $,$ and use the samples to estimate the expected value of the payout. You need to report your Monte Carlo estimate and its standard error and also submit your code in jupyter notebook. Speed does matter. I will provide you $3$ different solutions. The fastest of them takes only $0\mathrm{.}5$ seconds on my computer. You don$$t need to use any variance reduction techniques.