Distinguish between Logit model and Probit model. Explain with illustration the process involved in estimation of Logit model.

In applied econometrics, both the Logit and Probit models are used for modeling binary outcome variables. These models are essential for analyzing situations where the dependent variable is categorical and takes on two possible values, such as "yes" or "no," "success" or "failure." Although they serve similar purposes, they differ in their underlying assumptions and estimation techniques.

### Distinction Between Logit and Probit Models

1. Underlying Distribution:
   - Logit Model: Assumes that the error term in the model follows a logistic distribution. This distribution is characterized by its simplicity and the fact that it has heavier tails compared to the normal distribution. The logistic cumulative distribution function (CDF) is used to model the probability of the binary outcome.
   - Probit Model: Assumes that the error term follows a standard normal distribution. The CDF of the normal distribution is used to model the probability of the binary outcome.

2. Mathematical Formulation:
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