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Data Interview Question

Maximum Likelihood Estimation for Loan Default Risk

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Requirements Clarification & Assessment

  1. Objective:

    • Develop a model to predict the probability pp of loan default using historical data.
  2. Data Provided:

    • Historical outcomes of ten loans recorded as binary values: 0 for "no default" and 1 for "default".
    • Data: [0, 1, 0, 0, 1, 0, 0, 1, 0, 0].
  3. Assumptions:

    • Distribution: Assume the loan outcomes are independent and identically distributed (i.i.d.) Bernoulli trials, as each loan can either default or not.
    • Parameter: pp represents the probability of default for each loan.
  4. Tasks:

    • Derive the log-likelihood function for pp.
    • Compute the Maximum Likelihood Estimate (MLE) for pp.
  5. Constraints:

    • The solution should be based solely on the provided data without external datasets or assumptions beyond those stated.
  6. Performance Metrics:

    • Correctness of the MLE calculation.
    • Understanding of the log-likelihood function.
    • Ability to interpret results in the context of loan default risk.