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HTTP/1.1 200 OKx-amz-id-2: 8vpEpI5vm7Z5/RrqyuPSuyrNmIH83amtDsUu5UAlI3k5atat2W1fYE//uX/PvW43NT38mWzVHm+Td9Ww9trNEIotOOCcMePlx-amz-request-id: HSPD2F3NXAX5Q5R7Date: Mon, 16 Feb 2026 22:41:12 GMTLast-Modified: Sun, 18 May 2025 02:00:19 GMTETag: 7d7ceffba5e62df44a4a0a12c55e6b80Content-Type: text/htmlContent-Length: 34397Server: AmazonS3 !DOCTYPE html>html xmlnshttp://www.w3.org/1999/xhtml langen xml:langen>head>meta charsetutf-8>meta namegenerator contentquarto-1.5.57>meta nameviewport contentwidthdevice-width, initial-scale1.0, user-scalableyes>meta nameauthor contentAdam constantine>meta namedcterms.date content2025-01-01>title>MA2224/title>style>code{white-space: pre-wrap;}span.smallcaps{font-variant: small-caps;}div.columns{display: flex; gap: min(4vw, 1.5em);}div.column{flex: auto; overflow-x: auto;}div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;}ul.task-list{list-style: none;}ul.task-list li inputtypecheckbox { width: 0.8em; margin: 0 0.8em 0.2em -1em; /* quarto-specific, 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classsidebar-item-text sidebar-link> span classmenu-text>span classchapter-number>D/span> span classchapter-title>Datasets/span>/span>/a> /div>/li> li classsidebar-item> div classsidebar-item-container> a href./makeThisBook.html classsidebar-item-text sidebar-link> span classmenu-text>span classchapter-number>E/span> span classchapter-title>makeThisBook.html/span>/span>/a> /div>/li> li classsidebar-item> div classsidebar-item-container> a href./references.html classsidebar-item-text sidebar-link> span classmenu-text>span classchapter-number>F/span> span classchapter-title>References/span>/span>/a> /div>/li> /ul> /li> /ul> /div>/nav>div idquarto-sidebar-glass classquarto-sidebar-collapse-item data-bs-togglecollapse data-bs-target.quarto-sidebar-collapse-item>/div>!-- margin-sidebar --> div idquarto-margin-sidebar classsidebar margin-sidebar> nav idTOC roledoc-toc classtoc-active> h2 idtoc-title>Table of contents/h2> ul> li>a href#preface idtoc-preface classnav-link active data-scroll-target#preface>Preface/a>/li> /ul>/nav> /div>!-- main -->main classcontent idquarto-document-content>header idtitle-block-header classquarto-title-block default>div classquarto-title>h1 classtitle>MA2224/h1>/div>div classquarto-title-meta> div> div classquarto-title-meta-heading>Author/div> div classquarto-title-meta-contents> p>Adam constantine /p> /div> /div> div> div classquarto-title-meta-heading>Published/div> div classquarto-title-meta-contents> p classdate>January 1, 2025/p> /div> /div> /div> /header>section idpreface classlevel1 unnumbered>h1 classunnumbered>Preface/h1>p>img srcDSlogo.jpg titleMA2224 classquarto-cover-image img-fluid>/p>p>This is not really a book but instead a collection of lectures for MA2224 Probability and Statistics for Engineers taught at NYU Tandon School of Engineering. The presentation is slightly different with more details and narrative thrown in but the material is the same./p>p>If you have stumbled across this book randomly it may be helpful to know that it is designed for an introductory probability and statistics course with calculus 2 as a prerequisite. This means there will be many integration problems but only single-variable./p>p>The course itself does not include any use of a programming language but instructions and examples are provided in this “book” for whomever may be interested (see a href./pythonsetup.html>Python/a> and a href./Rsetup.html>R/a> )./p>p>If you find typos or want to email me for some reason you may at a hrefmailto:ac5597@nyu.edu>ac5597@nyu.edu/a>. I may or may not read/respond to emails./p>p>Below are the topics covered in this “book”, anything marked as optional is optional because either we only sometimes will teach or is part of the software lessons that arent covered in the class I teach./p>ul>li>a href./probability.html>Part 1: Probability/a> - Covers the probability ideas that are needed for the more interesting parts of the class.ul>li>Boring counting stuff/li>li>Probability rules/li>li>Bayes Theorem/li>li>Random Variables/li>li>Discrete Distributions/li>li>Continuous Distributions/li>li>Joint Distributions/li>li>Linear combinations of random variables/li>li>Moment Generating functions (Optional)/li>li>Likelihood functions (Optional)/li>/ul>/li>li>a href./statistics.html>Part 2: Data Analysis/a> - Covers the basic ideas of data analysis that will be helpful for the class. This will go more in depth than I will in MA2224/li>li>a href./samplingDistributions.html>Part 3: Sampling Distributions/a>/li>li>a href./inference.html>Part 4: Inference and Testing/a>/li>/ul>/section>/main> !-- /main -->script idquarto-html-after-body typeapplication/javascript>window.document.addEventListener(DOMContentLoaded, function (event) { const toggleBodyColorMode (bsSheetEl) > { const mode bsSheetEl.getAttribute(data-mode); const bodyEl window.document.querySelector(body); if (mode dark) { bodyEl.classList.add(quarto-dark); bodyEl.classList.remove(quarto-light); } else { bodyEl.classList.add(quarto-light); bodyEl.classList.remove(quarto-dark); } } const toggleBodyColorPrimary () > { const bsSheetEl window.document.querySelector(link#quarto-bootstrap); if (bsSheetEl) { toggleBodyColorMode(bsSheetEl); } } toggleBodyColorPrimary(); const icon ; const anchorJS new window.AnchorJS(); anchorJS.options { placement: right, icon: icon }; anchorJS.add(.anchored); const isCodeAnnotation (el) > { for (const clz of el.classList) { if (clz.startsWith(code-annotation-)) { return true; } } return false; } const onCopySuccess function(e) { // button target const button e.trigger; // dont keep focus button.blur(); // flash checked button.classList.add(code-copy-button-checked); var currentTitle button.getAttribute(title); button.setAttribute(title, Copied!); let tooltip; if (window.bootstrap) { button.setAttribute(data-bs-toggle, tooltip); button.setAttribute(data-bs-placement, left); button.setAttribute(data-bs-title, Copied!); tooltip new bootstrap.Tooltip(button, { trigger: manual, customClass: code-copy-button-tooltip, offset: 0, -8}); tooltip.show(); } setTimeout(function() { if (tooltip) { tooltip.hide(); button.removeAttribute(data-bs-title); button.removeAttribute(data-bs-toggle); button.removeAttribute(data-bs-placement); } button.setAttribute(title, currentTitle); button.classList.remove(code-copy-button-checked); }, 1000); // clear code selection e.clearSelection(); } const getTextToCopy function(trigger) { const codeEl trigger.previousElementSibling.cloneNode(true); for (const childEl of codeEl.children) { if (isCodeAnnotation(childEl)) { childEl.remove(); } } return codeEl.innerText; } const clipboard new window.ClipboardJS(.code-copy-button:not(data-in-quarto-modal), { text: getTextToCopy }); clipboard.on(success, onCopySuccess); if (window.document.getElementById(quarto-embedded-source-code-modal)) { // For code content inside modals, clipBoardJS needs to be initialized with a container option // TODO: Check when it could be a function (https://github.com/zenorocha/clipboard.js/issues/860) const clipboardModal new window.ClipboardJS(.code-copy-buttondata-in-quarto-modal, { text: getTextToCopy, container: window.document.getElementById(quarto-embedded-source-code-modal) }); clipboardModal.on(success, onCopySuccess); } var localhostRegex new RegExp(/^(?:http|https):\/\/localhost\:?0-9*\//); var mailtoRegex new RegExp(/^mailto:/); var filterRegex new RegExp(/ + window.location.host + /); var isInternal (href) > { return filterRegex.test(href) || localhostRegex.test(href) || mailtoRegex.test(href); } // Inspect non-navigation links and adorn them if external var links window.document.querySelectorAll(ahref:not(.nav-link):not(.navbar-brand):not(.toc-action):not(.sidebar-link):not(.sidebar-item-toggle):not(.pagination-link):not(.no-external):not(aria-hidden):not(.dropdown-item):not(.quarto-navigation-tool):not(.about-link)); for (var i0; ilinks.length; i++) { const link linksi; if (!isInternal(link.href)) { // undo the damage that might have been done by quarto-nav.js in the case of // links that we want to consider external if (link.dataset.originalHref ! 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null) { try { const html processXRef(id, note.cloneNode(true)); instance.setContent(html); } finally { instance.enable(); instance.show(); } } else { // See if we can fetch this fetch(url.split(#)0) .then(res > res.text()) .then(html > { const parser new DOMParser(); const htmlDoc parser.parseFromString(html, text/html); const note htmlDoc.getElementById(id); if (note ! null) { const html processXRef(id, note); instance.setContent(html); } }).finally(() > { instance.enable(); instance.show(); }); } } else { // See if we can fetch a full url (with no hash to target) // This is a special case and we should probably do some content thinning / targeting fetch(url) .then(res > res.text()) .then(html > { const parser new DOMParser(); const htmlDoc parser.parseFromString(html, text/html); const note htmlDoc.querySelector(main.content); if (note ! null) { // This should only happen for chapter cross references // (since there is no id in the URL) // remove the first header if (note.children.length > 0 && note.children0.tagName HEADER) { note.children0.remove(); } const html processXRef(null, note); instance.setContent(html); } }).finally(() > { instance.enable(); instance.show(); }); } }, function(instance) { }); } let selectedAnnoteEl; const selectorForAnnotation ( cell, annotation) > { let cellAttr data-code-cell + cell + ; let lineAttr data-code-annotation + annotation + ; const selector span + cellAttr + + lineAttr + ; return selector; } const selectCodeLines (annoteEl) > { const doc window.document; const targetCell annoteEl.getAttribute(data-target-cell); const targetAnnotation annoteEl.getAttribute(data-target-annotation); const annoteSpan window.document.querySelector(selectorForAnnotation(targetCell, targetAnnotation)); const lines annoteSpan.getAttribute(data-code-lines).split(,); const lineIds lines.map((line) > { return targetCell + - + line; }) let top null; let height null; let parent null; if (lineIds.length > 0) { //compute the position of the single el (top and bottom and make a div) const el window.document.getElementById(lineIds0); top el.offsetTop; height el.offsetHeight; parent el.parentElement.parentElement; if (lineIds.length > 1) { const lastEl window.document.getElementById(lineIdslineIds.length - 1); const bottom lastEl.offsetTop + lastEl.offsetHeight; height bottom - top; } if (top ! null && height ! null && parent ! null) { // cook up a div (if necessary) and position it let div window.document.getElementById(code-annotation-line-highlight); if (div null) { div window.document.createElement(div); div.setAttribute(id, code-annotation-line-highlight); div.style.position absolute; parent.appendChild(div); } div.style.top top - 2 + px; div.style.height height + 4 + px; div.style.left 0; let gutterDiv window.document.getElementById(code-annotation-line-highlight-gutter); if (gutterDiv null) { gutterDiv window.document.createElement(div); gutterDiv.setAttribute(id, code-annotation-line-highlight-gutter); gutterDiv.style.position absolute; const codeCell window.document.getElementById(targetCell); const gutter codeCell.querySelector(.code-annotation-gutter); gutter.appendChild(gutterDiv); } gutterDiv.style.top top - 2 + px; gutterDiv.style.height height + 4 + px; } selectedAnnoteEl annoteEl; } }; const unselectCodeLines () > { const elementsIds code-annotation-line-highlight, code-annotation-line-highlight-gutter; elementsIds.forEach((elId) > { const div window.document.getElementById(elId); if (div) { div.remove(); } }); selectedAnnoteEl undefined; }; // Handle positioning of the toggle window.addEventListener( resize, throttle(() > { elRect undefined; if (selectedAnnoteEl) { selectCodeLines(selectedAnnoteEl); } }, 10) ); function throttle(fn, ms) { let throttle false; let timer; return (...args) > { if(!throttle) { // first call gets through fn.apply(this, args); throttle true; } else { // all the others get throttled if(timer) clearTimeout(timer); // cancel #2 timer setTimeout(() > { fn.apply(this, args); timer throttle false; }, ms); } }; } // Attach click handler to the DT const annoteDls window.document.querySelectorAll(dtdata-target-cell); for (const annoteDlNode of annoteDls) { annoteDlNode.addEventListener(click, (event) > { const clickedEl event.target; if (clickedEl ! selectedAnnoteEl) { unselectCodeLines(); const activeEl window.document.querySelector(dtdata-target-cell.code-annotation-active); if (activeEl) { activeEl.classList.remove(code-annotation-active); } selectCodeLines(clickedEl); clickedEl.classList.add(code-annotation-active); } else { // Unselect the line unselectCodeLines(); clickedEl.classList.remove(code-annotation-active); } }); } const findCites (el) > { const parentEl el.parentElement; if (parentEl) { const cites parentEl.dataset.cites; if (cites) { return { el, cites: cites.split( ) }; } else { return findCites(el.parentElement) } } else { return undefined; } }; var bibliorefs window.document.querySelectorAll(aroledoc-biblioref); for (var i0; ibibliorefs.length; i++) { const ref bibliorefsi; const citeInfo findCites(ref); if (citeInfo) { tippyHover(citeInfo.el, function() { var popup window.document.createElement(div); citeInfo.cites.forEach(function(cite) { var citeDiv window.document.createElement(div); citeDiv.classList.add(hanging-indent); citeDiv.classList.add(csl-entry); var biblioDiv window.document.getElementById(ref- + cite); if (biblioDiv) { citeDiv.innerHTML biblioDiv.innerHTML; } popup.appendChild(citeDiv); }); return popup.innerHTML; }); } }});/script>nav classpage-navigation> div classnav-page nav-page-previous> /div> div classnav-page nav-page-next> a href./acknowledgment.html classpagination-link aria-labelAcknowledgment> span classnav-page-text>Acknowledgment/span> i classbi bi-arrow-right-short>/i> /a> /div>/nav>/div> !-- /content -->footer classfooter> div classnav-footer> div classnav-footer-left>p>NYU MA2224 Probability and Statistics for Engineers./p>/div> div classnav-footer-center> /div> div classnav-footer-right>p>This book was built with a hrefhttps://quarto.org/>Quarto/a>./p>/div> /div>/footer>/body>/html>
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