What This Document Is
This document contains solutions to the second homework assignment for Carnegie Mellon University’s Intermediate Statistics course (36-705), dated September 15, 2016. It provides detailed answers and justifications for a set of statistical problems.
Why This Document Matters
This document is intended for students enrolled in the course who are seeking to check their work and understand the correct approaches to the assigned problems. It serves as a key resource for self-assessment and clarifying any difficulties encountered while completing the homework. It’s most useful *after* a student has attempted the problems independently.
Common Limitations or Challenges
This document provides completed solutions, but does not offer step-by-step guidance on *how* to arrive at those solutions. It assumes the student has a foundational understanding of the concepts and is primarily seeking verification of their approach. It does not substitute for attending lectures or actively engaging with the course material.
What This Document Provides
The full document includes complete solutions for four problems:
* Problem 1: Explores properties of sub-Gaussian random variables.
* Problem 2: Applies Bernstein’s inequality to demonstrate the convergence rate of a sample mean.
* Problem 3: Presents counterexamples to disprove several claims regarding the order of magnitude of random variables.
* Problem 4: Demonstrates the relationship between a uniform random variable and a continuous cumulative distribution function.
This preview does *not* include the detailed mathematical derivations or proofs contained within the solutions themselves.
