MLE for Default Prediction

Assume you’re a data scientist for a bank and you’re tasked with building a model to estimate the probability of default on new loans. This parameter we’ll call p. You have historical data of loans with each loan’s outcome coded as 0 for “no default” and 1 for “default”.

Assume that, for the last ten loans, the data is the following: [0, 1, 0, 0, 1, 0, 0, 1, 0, 0].

Be sure to state any assumptions you’re making, such as assumptions about the distribution the observations are sampled from.

Estimate the following using the historical data given above:

• The log-likelihood function for the parameter p
• The MLE for the parameter p