{"id":16531,"date":"2019-12-28T18:30:07","date_gmt":"2019-12-28T23:30:07","guid":{"rendered":"http:\/\/bangla.salearningschool.com\/recent-posts\/test-estimation-tracking-probability-data-science\/"},"modified":"2020-02-08T09:40:33","modified_gmt":"2020-02-08T14:40:33","slug":"test-estimation-tracking-probability-data-science","status":"publish","type":"post","link":"http:\/\/bangla.sitestree.com\/?p=16531","title":{"rendered":"Test: Estimation, Tracking, Probability, Data Science"},"content":{"rendered":"

Chebyshev’s inequality<\/strong><\/p>\n

"In probability theory<\/a>, Chebyshev’s inequality<\/strong> (also called the Bienaym\u00e9\u2013Chebyshev inequality<\/strong>) guarantees that, for a wide class of probability distributions<\/a>, no more than a certain fraction of values can be more than a certain distance from the mean<\/a>.<\/p>\n

Specifically, no more than 1\/k<\/em>2 of the distribution’s values can be more than k<\/em> standard deviations<\/a> away from the mean<\/p>\n

(or equivalently, at least 1 \u2212 1\/k<\/em>2 of the distribution’s values are within k<\/em> standard deviations of the mean).<\/p>\n

The inequality has great utility because it can be applied to any probability distribution in which the mean and variance are defined. "<\/p>\n

https:\/\/en.wikipedia.org\/wiki\/Chebyshev%27s_inequality<\/a><\/p>\n

"Probabilistic statement[edit<\/a>]<\/span><\/h3>\n

Let X<\/em> (integrable) be a random variable<\/a> with finite expected value<\/a> \u03bc<\/em> and finite non-zero variance<\/a> \u03c3<\/em>2. Then for any real number<\/a> k<\/em> > 0,<\/p>\n

{\\displaystyle \\Pr(|X-\\mu |\\geq k\\sigma )\\leq {\\frac {1}{k^{2}}}.}\"\\Pr(|X-\\mu<\/p>\n

Only the case {\\displaystyle k>1}\"k is useful. When {\\displaystyle k\\leq 1}\"{\\displaystyle the right-hand side {\\displaystyle {\\frac {1}{k^{2}}}\\geq 1}\"{\\displaystyle and the inequality is trivial as all probabilities are \u2264 1."<\/p>\n

"As an example, using \"{\\displaystyle shows that the probability that values lie outside the interval \"{\\displaystyle does not exceed \"{\\frac."<\/p>\n

"Markov’s inequality <\/strong><\/p>\n

"Markov’s inequality (and other similar inequalities) relate probabilities to expectations<\/a>, and provide (frequently loose but still useful) bounds for the cumulative distribution function<\/a> of a random variable."<\/p>\n

Statement[edit<\/a>]<\/span><\/h2>\n

If X is a nonnegative random variable and a<\/em> > 0, then the probability that X is at least a is at most the expectation of X divided by a:[1]<\/a><\/p>\n

{\\displaystyle \\operatorname {P} (X\\geq a)\\leq {\\frac {\\operatorname {E} (X)}{a}}.}\"{\\displaystyle<\/p>\n

Sayed Ahmed<\/strong>
\n<\/em><\/p>\n

BSc. Eng. in Comp. Sc. & Eng. (BUET)<\/strong><\/em>
\nMSc. in Comp. Sc. (U of Manitoba, Canada)<\/strong><\/em>
\nMSc. in Data Science and Analytics (Ryerson University, Canada)<\/strong><\/em>
\nLinkedin<\/strong>: https:\/\/ca.linkedin.com\/in\/sayedjustetc<\/a>
\n<\/em><\/p>\n

Blog<\/strong>: http:\/\/Bangla.SaLearningSchool.com<\/a>, http:\/\/SitesTree.com<\/a> <\/em>
\nOnline and Offline Training<\/strong>: http:\/\/Training.SitesTree.com<\/a> <\/em><\/p>\n

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Chebyshev’s inequality "In probability theory, Chebyshev’s inequality (also called the Bienaym\u00e9\u2013Chebyshev inequality) guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from the mean. Specifically, no more than 1\/k2 of the distribution’s values can be more than k standard deviations … <\/p>\n

Continue reading<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1910,182],"tags":[],"class_list":["post-16531","post","type-post","status-publish","format-standard","hentry","category-ai-ml-ds-rl-dl-nn-nlp-data-mining-optimization","category---blog","item-wrap"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack-related-posts":[{"id":16532,"url":"http:\/\/bangla.sitestree.com\/?p=16532","url_meta":{"origin":16531,"position":0},"title":"Part 1: Some Math\/Stat Background that (true) Data Scientists will know\/use: from the internet","author":"Sayed","date":"December 28, 2019","format":false,"excerpt":"Chebyshev's inequality \"In probability theory, Chebyshev's inequality (also called the Bienaym\u00e9\u2013Chebyshev inequality) guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from the mean. Specifically, no more than 1\/k2 of the distribution's values can be\u2026","rel":"","context":"In "Math and Statistics for Data Science, and Engineering"","block_context":{"text":"Math and Statistics for Data Science, and Engineering","link":"http:\/\/bangla.sitestree.com\/?cat=1908"},"img":{"alt_text":"","src":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/8\/85\/Discrete_probability_distrib.svg\/220px-Discrete_probability_distrib.svg.png","width":350,"height":200},"classes":[]},{"id":16536,"url":"http:\/\/bangla.sitestree.com\/?p=16536","url_meta":{"origin":16531,"position":1},"title":"Part 2: Some basic Math\/Statistics concepts that Data Scientists (the true ones) will usually know\/use","author":"Sayed","date":"December 29, 2019","format":false,"excerpt":"Part 2: Some basic Math\/Statistics concepts that Data Scientists (the true ones) will usually know\/use (came across, studied, learned, used) Covariance and Correlation \"Covariance is a measure of how two variables change together, but its magnitude is unbounded, so it is difficult to interpret. By dividing covariance by the product\u2026","rel":"","context":"In "Math and Statistics for Data Science, and Engineering"","block_context":{"text":"Math and Statistics for Data Science, and Engineering","link":"http:\/\/bangla.sitestree.com\/?cat=1908"},"img":{"alt_text":"[eq5]","src":"https:\/\/i0.wp.com\/www.statlect.com\/images\/covariance-formula__12.png?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":17441,"url":"http:\/\/bangla.sitestree.com\/?p=17441","url_meta":{"origin":16531,"position":2},"title":"MISC STATistic PROBability LINEAR ALGebra MATRIX","author":"Sayed","date":"September 14, 2020","format":false,"excerpt":"MISC STAT PROB LINEAR ALG MATRIX PDF AND Stock and Bell Curve: https:\/\/www.investopedia.com\/terms\/p\/pdf.asp PDF in Khan Academy: https:\/\/www.khanacademy.org\/math\/statistics-probability\/random-variables-stats-library\/random-variables-continuous\/v\/probability-density-functions Mixed Random Variable https:\/\/www.youtube.com\/watch?v=ZXJjuRAXMhE \"The variance and the standard deviation are measures of the spread of the data around the mean. They summarise how close each observed data value is to the\u2026","rel":"","context":"In "\u09ac\u09cd\u09b2\u0997 \u0964 Blog"","block_context":{"text":"\u09ac\u09cd\u09b2\u0997 \u0964 Blog","link":"http:\/\/bangla.sitestree.com\/?cat=182"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":16434,"url":"http:\/\/bangla.sitestree.com\/?p=16434","url_meta":{"origin":16531,"position":3},"title":"Stochastic Processes and Related Terms","author":"Sayed","date":"November 27, 2019","format":false,"excerpt":"What is a Random Variable? 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