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