Problem $1$: Vehicle Fuel Efficiency Classification

Problem Description:

You are tasked with classifying vehicles as "Fuel Efficient" or "Not Fuel Efficient" using Naive Bayes classification. You need to estimate the conditional probabilities for different attributes and the class variable "Fuel Efficiency."

Exercises:

$1.$ Calculate Prior Probabilities: Calculate the prior probabilities of a vehicle being "Fuel Efficient" or "Not Fuel Efficient" based on the provided dataset.

$2.$ Conditional Probabilities for Nominal Attributes $($Vehicle Type and Fuel Type$)$: Calculate the conditional probabilities of a vehicle being "Fuel Efficient" or "Not Fuel Efficient" based on the vehicle type and fuel type $($Nominal attributes$).$

$3.$ Conditional Probabilities for Continuous Attributes $($Engine Size and Mileage$)$: Calculate the conditional probabilities of a vehicle being "Fuel Efficient" or "Not Fuel Efficient" based on engine size and mileage $($Continuous attributes$).$ You can assume Gaussian distributions.

$4.$ Conditional Probabilities for Ordinal Attributes $($Safety Rating$)$: Calculate the conditional probabilities of a vehicle being "Fuel Efficient" or "Not Fuel Efficient" based on the safety rating $($Ordinal attribute$).$

$5.$ Fuel Efficiency Classification: Given a new vehicle with the following attributes:

Vehicle Type: Hatchback

Engine Size: $1\mathrm{.}8$

Fuel Type: Gasoline

Mileage: $40\mathrm{.}2$

Safety Rating: Medium

To classify this vehicle as "Fuel Efficient" or "Not Fuel Efficient," use Naive Bayes and the conditional probabilities calculated in previous steps.