Maximum Likelihood Estimation for Loan Default Risk

Imagine you are a data scientist at a financial institution, tasked with creating a model to predict the likelihood of loan defaults. This probability will be denoted as p. You have access to historical loan data, where each loan outcome is recorded as 0 for "no default" and 1 for "default." Consider the data from the last ten loans: [0, 1, 0, 0, 1, 0, 0, 1, 0, 0]. Clearly outline any assumptions you make, such as those regarding the distribution from which the observations are drawn. Using the provided historical data, estimate the following: 1. The log-likelihood function for the parameter p 2. The Maximum Likelihood Estimate (MLE) for the parameter p