https://abaj.ai/tags/dobson/Recent content in Dobson on Aayush Bajaj's Augmenting InfrastructureHugoen© 2026 Aayush BajajMon, 31 Aug 2026 02:09:19 +1000https://abaj.ai/words/library/books/an_introduction_to_generalized_linear_models/Sun, 14 Jun 2026 13:42:58 +1100https://abaj.ai/words/library/books/an_introduction_to_generalized_linear_models/<p>Solutions to every exercise in the fourth edition of Dobson &amp; Barnett&rsquo;s <em>An Introduction to Generalized Linear Models</em> (Chapman &amp; Hall/CRC, 2018) — 78 exercises across 14 chapters, worked in R with the book&rsquo;s own datasets from the <code>dobson</code> package, with executed code and committed output throughout. This is the MATH5806 text; the book is filed at <a href="https://abaj.ai/roam/dobson_glm/" >An Introduction to Generalized Linear Models (Dobson &amp; Barnett)</a>.</p> <script type="text/javascript" src= '/js/pdf-js/build/pdf.js'></script> <style> #embed-pdf-container { position: relative; width: 100%; height: auto; min-height: 20vh; } .pdf-canvas { border: 1px solid black; direction: ltr; width: 100%; height: auto; display: none; } #the-canvas { border: 1px solid black; direction: ltr; width: 100%; height: auto; display: none; } .pdf-loadingWrapper { display: none; justify-content: center; align-items: center; width: 100%; height: 350px; } .pdf-loading { display: inline-block; width: 50px; height: 50px; border: 3px solid #d2d0d0;; border-radius: 50%; border-top-color: #383838; animation: spin 1s ease-in-out infinite; -webkit-animation: spin 1s ease-in-out infinite; } #overlayText { word-wrap: break-word; display: grid; justify-content: end; } #overlayText svg { height: clamp(1em, 2vw, 1.4em); 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text-align: center; line-height: 1.5rem; margin-right: 8px; padding: 0; } [data-theme="dark"] .toggle-button { color: white; } .toggle-button:focus { outline: none; } .collapsible-content { display: none; margin-left: 8px; margin-bottom: 0px; padding: 2px 0 2px 12px; border-left: 1px solid rgba(0, 0, 0, 0.1); transition: all 0.3s ease-out; } [data-theme="dark"] .collapsible-content { border-left-color: rgba(255, 255, 255, 0.12); } .collapsible-content.show { display: block; } </style> <script src="https://abaj.ai/js/collapsible-global.js"></script> </div> <h2 id="introduction">Introduction<a href="#introduction" class="post-heading__anchor" aria-hidden="true">#</a> </h2> <div class="collapsible-container"> <script type="text/javascript"> var folded = 'true'; </script> </div> <h3 id="problem-1-dot-1-let-y1-and-y2-be-independent-random-variables-with">Problem 1.1 — Let Y1 and Y2 be independent random variables with<a href="#problem-1-dot-1-let-y1-and-y2-be-independent-random-variables-with" class="post-heading__anchor" aria-hidden="true">#</a> </h3> <div class="math-problem" id="1.1"> <div class="math-problem-header"> <div class="problem-header-left"> <strong>Problem<span class="problem-counter"></span></strong> <span class="problem-name">(1.1)</span> </div> </div> <div class="math-problem-content"> <p>Let \(Y_1\) and \(Y_2\) be independent random variables with \(Y_1 \sim N(1,3)\) and \(Y_2 \sim N(2,5)\). If \(W_1 = Y_1 + 2Y_2\) and \(W_2 = 4Y_1 - Y_2\), what is the joint distribution of \(W_1\) and \(W_2\)? (difficulty: \(\star\))</p>