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Introduction to Data Science (DS 215)
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Module 3
Asymptotic Theory and Simulation
1
Deriving WLLN with Chebyshev's Inequality
Derive the Weak Law of Large Numbers (WLLN) using Chebyshev's inequality.
2
Proving the Central Limit Theorem with Characteristic Functions
Outline the proof of the Central Limit Theorem (CLT) using characteristic functions.
Probability vs. Almost Sure Convergence
Explain the conceptual difference between convergence in probability and almost sure convergence.
4
Linear Combinations of Independent Gaussian Random Variables
Prove that a linear combination of independent Gaussian random variables remains Gaussian.
5
Simulating CLT & Law of Large Numbers in Python
Project: Develop a Python simulation to visually demonstrate the Central Limit Theorem and the Law of Large Numbers.
Previous module
Probability Models for Data
Next module
Foundations of Statistical Inference