Probability-and-Distribution-Theory/index.html at master · SaiSampathKedari/Probability-and-Distribution-Theory · GitHub

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  <title>Probability and Distribution Theory | Casella-Berger | Sai Sampath Kedari</title>
  <meta name="description" content="Lecture notes and solved problems from Casella-Berger Statistical Inference (Ch.1–5). Foundations in Probability, Distributions, and Statistical Inference for Machine Learning, AI, and Robotics.">
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    <h1>Probability and Distribution Theory — Casella-Berger</h1>
    <p>This repository contains my <strong>lecture notes</strong> and <strong>solved problems</strong> from <em>Casella-Berger: Statistical Inference (Chapters 1–5)</em>, focused on foundational concepts in <strong>Probability Theory</strong> and <strong>Statistical Inference</strong>. These topics form the mathematical basis for <strong>Machine Learning</strong>, <strong>AI</strong>, and <strong>Robotics</strong>.</p>

    <h2>Key Topics Covered</h2>
    <ol>
      <li><strong>Probability Theory</strong>: Set theory, cardinality & countability, probability spaces, Borel sets, and Lebesgue measure.</li>
      <li><strong>Transformations & Expectations</strong>: Distributions of functions, moment-generating functions.</li>
      <li><strong>Common Families of Distributions</strong>: Discrete & continuous distributions, exponential families, inequalities.</li>
      <li><strong>Multiple Random Variables</strong>: Joint & marginal distributions, conditional distributions, mixture models.</li>
      <li><strong>Properties of a Random Sample</strong>: Sample mean, variance, order statistics, convergence, and random sampling.</li>
    </ol>

    <h2>Repository Structure</h2>
    <ul>
      <li><strong>Lecture Notes</strong>: Theoretical concepts and theorems.</li>
      <li><strong>Problem Sets</strong>: Solutions to <em>Casella-Berger</em> exercises for deeper understanding.</li>
    </ul>

    <h2>Purpose</h2>
    <p>These notes and solutions reflect my pursuit of strong mathematical foundations in <strong>Statistical Inference</strong> — the backbone of <strong>Monte Carlo Methods</strong>, <strong>Bayesian Filtering</strong>, and <strong>State Estimation</strong> in robotics and control.
       I plan to rewrite these in LaTeX for clarity and professional presentation.</p>

    <h2>About Me</h2>
    <p>I’m focused on building rigorous mathematical intuition to support my work in <strong>Robotics & AI Research</strong>.</p>

    <h2>Contact</h2>
    <p>
      📧 <a href="mailto:sampath@umich.edu">sampath@umich.edu</a><br>
      🔗 <a href="https://www.linkedin.com/in/sai-sampath-kedari" target="_blank">LinkedIn</a><br>
      🧠 <a href="https://github.com/SaiSampathKedari/Probability-and-Distribution-Theory" target="_blank">View Repository on GitHub</a>
    </p>

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      <p>© <span id="y"></span> Sai Sampath Kedari | Probability & Distribution Theory — Casella Berger | UMich STATS 510/511</p>
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