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Abstract

0/1*IvcwScIFWDfY2c0IVboVNQ.png"><figcaption></figcaption></figure><figure id="e604"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*6bFeeOMjWYzJuRO7sXjFjw.png"><figcaption></figcaption></figure><figure id="f73d"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*CLhU9VAolL3AcV3McV_bTQ.png"><figcaption></figcaption></figure><figure id="b261"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*AH6BG2mVTkCHb_XGKGdpcw.png"><figcaption></figcaption></figure><h2 id="ceae">Important Discrete Probability Distributions</h2><figure id="5c6d"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*fLbdhQaewZkyASujsYr4Zg.png"><figcaption></figcaption></figure><figure id="560b"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*6-W1YW7rG0nzDr_FMacd_Q.png"><figcaption></figcaption></figure><figure id="7f72"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*bf8_XLBcNBcF8PvaWg8ySQ.png"><figcaption></figcaption></figure><figure id="77e1"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*IBm8azLHAvLclHGTCZX-NQ.png"><figcaption></figcaption></figure><figure id="e95e"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*WaIJEE0sM1_H3vCECLPzRA.png"><figcaption></figcaption></figure><figure id="1fbc"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*J6IqsX5bzeL4bpxzBNQp7A.png"><figcaption></figcaption></figure><figure id="06c7"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*e1BXDgb4WkH9q7p_rLbWug.png"><figcaption></figcaption></figure><h2 id="e699">Important Continous Probability Distributions</h2><figure id="443e"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*FqkNn9Wx4WvYX8lb_azxXA.png"><figcaption></figcaption></figure><figure id="4b91"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*qv-FIM-uPziVQhzrxTxGTQ.png"><figcaption></figcaption></figure><figure id="a24c"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*bO01kNIcnBpVDqNTpMbS8A.png"><figcaption></figcaption></figure><figure id="b219"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*QB2HSPjKLocLaYYIlZY5Eg.png"><figcaption></figcaption></figure><figure id="dcf0"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*jj8IuS2bqkR8tohu7hatuw.png"><figcaption></figcaption></figure><figure id="a217"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*xdiB4z2dFy_kd4z_TwZsuQ.png"><figcaption></figcaption></figure><figure id="fa55"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*haAJehSjdsumlfFskwTIFw.png"><figcaption></figcaption></figure><figure id="5724"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*nqKH7JO7AwUjWEbujyLY1A.png"><figcaption></figcaption></figure><figure id="1dc2"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*jFdJlfs0IkmGILNpdelo2w.png"><figcaption></figcaption></figure><h2 id="eea1">Random Vectors</h2><figure id="d099"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*_aUOzTFJRTzCc6oSlaBL9w.png"><figcaption></figcaption></figure><figure id="a558"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*UkEgKxIVVnLRiUFnJpeEmg.png"><figcaption></figcaption></figure><figure id="489d"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*5PBcTey6dPgjFc067Y8gzg.png"><figcaption></figcaption></figure><h2 id="79a9">CDF’s, Joint P

Options

MF’s and PDF’d Marginal and Conditional Distributions, and independence.</h2><figure id="b9d6"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*cFF8ciRGMlgyapRhcK_jZg.png"><figcaption></figcaption></figure><figure id="87c1"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*WV8c0fJkVO9A8yS7eiH2zQ.png"><figcaption></figcaption></figure><figure id="e5bb"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*hYrD8vtPYGgsWurXx53kQg.png"><figcaption></figcaption></figure><figure id="56ba"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*6LRV4o8MYJPpcThXGJvCEg.png"><figcaption></figcaption></figure><figure id="80cd"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*vOvPR3hRh1NsIDEfClzxZw.png"><figcaption></figcaption></figure><figure id="4ad0"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*RzZLKJXroKroOav-cAfiwg.png"><figcaption></figcaption></figure><figure id="c07b"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*Y5N0LKqV4t3iMws2zAV6EA.png"><figcaption></figcaption></figure><h2 id="7b42">Law of Total Probability, Baye’s Theorem and LOE</h2><figure id="1001"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*NJ670FCSJfjQ3EdYBjpSOw.png"><figcaption></figcaption></figure><figure id="0fa0"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*hAL3rLjiraCg-DCpBcLi9A.png"><figcaption></figcaption></figure><figure id="7a5b"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*8IcjqfIDt47sfh5lo5P46Q.png"><figcaption></figcaption></figure><figure id="6910"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*IES4MS-yHj33UapstLW7uA.png"><figcaption></figcaption></figure><h2 id="cf2c">Important Multivariate Distributions</h2><figure id="6429"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*u2TLZXMJeSoGZLJZuDNciA.png"><figcaption></figcaption></figure><figure id="ea3d"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*YKDMLa0j8CfuEKc_DAVcfg.png"><figcaption></figcaption></figure><figure id="6a26"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*E_Gu3qz5cMW_b0mgOlb0WA.png"><figcaption></figcaption></figure><figure id="38c1"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*UkRKqkKoMrsyHXa2LDUW7w.png"><figcaption></figcaption></figure><h2 id="a32f">Main page</h2><div id="c486" class="link-block"> <a href="https://readmedium.com/a-complete-introduction-to-time-series-analysis-with-r-9882f2d44c9d"> <div> <div> <h2>A Complete Introduction To Time Series Analysis (with R)</h2> <div><h3>During these times of the Covid19 pandemic, you have perhaps heard about the collaborative efforts to predict new…</h3></div> <div><p>medium.com</p></div> </div> <div> <div style="background-image: url(https://miro.readmedium.com/v2/resize:fit:320/1*TL2PeOANEN4zG0_OqoHptQ.jpeg)"></div> </div> </div> </a> </div><h2 id="74ff">Follow me at</h2><ol><li><a href="https://www.linkedin.com/in/hair-parra-526ba19b/">https://www.linkedin.com/in/hair-parra-526ba19b/</a></li><li><a href="https://github.com/JairParra">https://github.com/JairParra</a></li><li><a href="https://medium.com/@hair.parra">https://medium.com/@hair.parra</a></li></ol></article></body>

Appendix: Probability

These notes are intended to provide a “fast” collection of theoretical definitions, theorems, and concepts for Probability as a refresher and a collection of definitions, theorems, and corollaries only, and as an Appendix to my “A Complete Introduction to Time Series Analysis” series. Although some proofs are provided, no examples are provided, so if you are looking for a more comprehensive guide, please consider reading this C229 Probability Review.

Note: Since I might sometimes make changes on this page by adding/updating some theorems, etc. the number of each item might not be in order or repeated. This will not be the case in the actual book~. Please don’t mind it too much!

Probability Spaces

PMF’s. , PDF’s and CDF’s

Expectation, Variance, Covariance, Correlation, and identities

Cauchy-Shwartz, Markov’s, and Chevisheff’s Inequalities

Important Discrete Probability Distributions

Important Continous Probability Distributions

Random Vectors

CDF’s, Joint PMF’s and PDF’d Marginal and Conditional Distributions, and independence.

Law of Total Probability, Baye’s Theorem and LOE

Important Multivariate Distributions

Main page

Follow me at

  1. https://www.linkedin.com/in/hair-parra-526ba19b/
  2. https://github.com/JairParra
  3. https://medium.com/@hair.parra
Probability
Statistics
Machine Learning
Mathematics
Math
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