Machine Learning Foundations Week 11 Graded Assignment Solutions

💻 Machine Learning Foundations Week 11 Graded Assignment Solutions

Version: v2_t12024_GradeBoost — Master the probabilistic foundations of ML with detailed guides on random variables, expectation, and joint probability distributions.

This downloadable PDF provides complete, verified solutions for the eleventh week of the Machine Learning Foundations course. These solutions are essential for mastering the statistics and probability theory used to model uncertainty and evaluate predictive confidence in machine learning.

Detailed Question Summary

The solution provides the technical logic and step-by-step mathematical proofs for the following advanced problems:

• Q1 – Q2: Continuous Random Variables — Solving for unknown constants in Probability Density Functions (PDFs) and calculating interval probabilities using integration.
• Q3: Joint Probability Distributions — Analyzing multi-variable PDF tables to identify valid joint probabilities and marginal distribution requirements.
• Q4: Conditional Probability Axioms — Verifying fundamental laws including complements, subset properties, and empty set probabilities for multiple events.
• Q5: Independent vs. Dependent Events — Mathematical proof of independence through intersection products \( P(A \cap B) = P(A)P(B) \).
• Q6: Geometric Distribution Logic — Calculating the probability of success within a specific number of trials (e.g., dice throws) using cumulative geometric sequences.
• Q7: Statistical Independence Analysis — Testing if the product of marginal probabilities matches the joint PMF value to determine variable dependency.
• Q8: Expectation of Discrete Variables — Solving for distribution parameters given a target expected value \( E(X) \) and the total sum of probabilities.