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  3. Statistical Thinking in Python (Part 1)

Exercise

Sampling out of the Binomial distribution

Compute the probability mass function for the number of defaults we would expect for 100 loans as in the last section, but instead of simulating all of the Bernoulli trials, perform the sampling using rng.binomial(). This is identical to the calculation you did in the last set of exercises using your custom-written perform_bernoulli_trials() function, but far more computationally efficient. Given this extra efficiency, we will take 10,000 samples instead of 1000. After taking the samples, plot the CDF as last time. This CDF that you are plotting is that of the Binomial distribution.

Note: For this exercise and all going forward, the random number generator is instantiated and seeded for you (with rng = np.random.default_rng(42)) to save you typing that each time.

Instructions

100 XP
  • Draw samples out of the Binomial distribution using rng.binomial(). You should use parameters n = 100 and p = 0.05, and set the size keyword argument to 10000.
  • Compute the CDF using your previously-written ecdf() function.
  • Plot the CDF with axis labels. The x-axis here is the number of defaults out of 100 loans, while the y-axis is the CDF.
  • Show the plot.