Exercise

How many defaults might we expect?

Let's say a bank made 100 mortgage loans. It is possible that anywhere between 0 and 100 of the loans will be defaulted upon. You would like to know the probability of getting a given number of defaults, given that the probability of a default is p = 0.05. To investigate this, you will do a simulation. You will perform 100 Bernoulli trials using the perform_bernoulli_trials() function you wrote in the previous exercise and record how many defaults we get. Here, a success is a default. (Remember that the word "success" just means that the Bernoulli trial evaluates to True, i.e., did the loan recipient default?) You will do this for another 100 Bernoulli trials. And again and again until we have tried it 1000 times. Then, you will plot a histogram describing the probability of the number of defaults.

Instructions

100 XP
  • Seed the random number generator to 42.
  • Initialize n_defaults, an empty array, using np.empty(). It should contain 1000 entries, since we are doing 1000 simulations.
  • Write a for loop with 1000 iterations to compute the number of defaults per 100 loans using the perform_bernoulli_trials() function. It accepts two arguments: the number of trials n - in this case 100 - and the probability of success p - in this case the probability of a default, which is 0.05. On each iteration of the loop store the result in an entry of n_defaults.
  • Plot a histogram of n_defaults. Include the density=True keyword argument so that the height of the bars of the histogram indicate the probability.
  • Show your plot.