{"id":891,"date":"2016-05-30T21:51:03","date_gmt":"2016-05-30T21:51:03","guid":{"rendered":"http:\/\/www.inspirenignite.com\/jntuh\/?p=891"},"modified":"2021-10-27T21:29:17","modified_gmt":"2021-10-27T21:29:17","slug":"jntuh-b-tech-2nd-year-1-sem-electronics-and-communications-engineering-2-1-probability-theory-and-stochastic-processes-engineering-r13","status":"publish","type":"post","link":"https:\/\/www.inspirenignite.com\/jntuh\/jntuh-b-tech-2nd-year-1-sem-electronics-and-communications-engineering-2-1-probability-theory-and-stochastic-processes-engineering-r13\/","title":{"rendered":"JNTUH B.Tech 2nd Year 1 sem Electronics and Communications Engineering (2-1) Probability Theory and Stochastic Processes Engineering R13."},"content":{"rendered":"<p>JNTUH B.Tech 2nd year Probability Theory and Stochastic Processes gives you detail information about Probability Theory and Stochastic Processes Engineering R13 year subject. It will be help full you to understand you complete curriculum of the year.<\/p>\n<p><strong>Objectives<\/strong><\/p>\n<p>The primary objective of this course is:<\/p>\n<ul>\n<li>To provide mathematical background and sufficient experience so that the student can read, write, and\u00a0understand sentences in the language of probability theory, as well as solve probabilistic problems in\u00a0signal processing and Communication Engineering.<\/li>\n<li>To introduce students to the basic methodology of \u201cprobabilistic thinking\u201d and to apply it to problems;<\/li>\n<li>To understand basic concepts of probability theory and random variables, how to deal with multiple\u00a0andom variables, Conditional probability and conditional expectation, joint distribution and\u00a0independence, mean square estimation.<\/li>\n<li>To understand the difference between time averages and statistical averages<\/li>\n<li>Analysis of random process and application to the signal processing in the communication system.<\/li>\n<li>To teach students how to apply sums and integrals to compute probabilities, means, and expectations.<\/li>\n<\/ul>\n<p><strong>UNIT-I<\/strong><\/p>\n<p>Probability and Random Variable Probability: Probability introduced through Sets and Relative Frequency, Experiments and Sample Spaces, Discrete and Continuous Sample Spaces, Events, Probability Definitions and Axioms, Mathematical Model of Experiments, Probability as a Relative Frequency, Joint Probability, Conditional Probability, Total Probability,\u00a0Bayes\u2019 Theorem, Independent Events.\u00a0Random Variable: Definition of a Random Variable, Conditions for a Function to be a Random Variable,\u00a0Discrete, Continuous and Mixed Random Variables<\/p>\n<p><strong>UNIT -II<\/strong><\/p>\n<p>Distribution &amp; Density Functions and Operation on One Random Variable \u2013 Expectations\u00a0Distribution &amp; Density Functions: Distribution and Density functions and their Properties &#8211; Binomial, Poisson,\u00a0Uniform, Gaussian, Exponential, Rayleigh and Conditional Distribution, Methods of defining Conditional Event,\u00a0Conditional Density, Properties.\u00a0Operation on One Random Variable \u2013 Expectations: Introduction, Expected Value of a Random Variable,\u00a0Function of a Random Variable, Moments about the Origin, Central Moments, Variance and Skew, Chebychev\u2019s\u00a0Inequality, Characteristic Function, Moment Generating Function, Transformations of a Random Variable:\u00a0Monotonic Transformations for a Continuous Random Variable, Non-monotonic Transformations of Continuous\u00a0Random Variable, Transformation of a Discrete Random Variable.<\/p>\n<p><strong>UNIT-III<\/strong><\/p>\n<p>Multiple Random Variables and Operations Multiple Random Variables: Vector Random Variables, Joint Distribution Function, Properties of Joint Distribution, Marginal Distribution Functions, Conditional Distribution and Density \u2013 Point Conditioning, Conditional Distribution and Density \u2013Interval conditioning, Statistical Independence, Sum of Two Random Variables, Sum of Several Random Variables, Central Limit Theorem (Proof not expected), Unequal Distribution, Equal Distributions.\u00a0Operations on Multiple Random Variables: Expected Value of a Function of Random Variables: Joint \u00a0Moments about the Origin, Joint Central Moments, Joint Characteristic Functions, Jointly Gaussian Random\u00a0Variables: Two Random Variables case, N Random Variable case, Properties, Transformations of Multiple\u00a0Random Variables, Linear Transformations of Gaussian Random Variables.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/play.google.com\/store\/apps\/details?id=ini.istudy\" target=\"_blank\" rel=\"noopener\"><strong><em><span style=\"color: #ff0000\">Download iStudy Android App for complete JNTUH syllabus, results, timetables and all other updates. There are no ads and no pdfs and will make your life way easier<\/span>.<\/em><\/strong><\/a><\/p>\n<p><strong>TEXT BOOKS\u00a0<\/strong><\/p>\n<ol>\n<li>Probability, Random Variables &amp; Random Signal Principles &#8211; Peyton Z. Peebles, 4Ed., 2001, TMH.<\/li>\n<li>Probability and Random Processes \u2013 Scott Miller, Donald Childers, 2 Ed, Elsevier, 2012.<\/li>\n<\/ol>\n<p><strong>REFERENCE BOOKS<\/strong><\/p>\n<ol>\n<li>Probability, Random Variables and Stochastic Processes \u2013 Athanasios Papoulis and S. Unnikrishna\u00a0Pillai, 4 Ed., TMH.<\/li>\n<li>Theory of Probability and Stochastic Processes- Pradip Kumar Gosh, University Press<\/li>\n<li>Probability and Random Processes with Application to Signal Processing \u2013 Henry Stark and John W.\u00a0Woods, 3 Ed., PE<\/li>\n<li>Probability Methods of Signal and System Analysis &#8211; George R. Cooper, Clave D. MC Gillem, 3 Ed.,\u00a01999, Oxford.<\/li>\n<li>Statistical Theory of Communication &#8211; S.P. Eugene Xavier, 1997, New Age Publications.<\/li>\n<\/ol>\n<p><strong>Outcomes<\/strong><\/p>\n<ul>\n<li>Upon completion of the subject, students will be able to compute:<\/li>\n<li>Simple probabilities using an appropriate sample space.<\/li>\n<li>Simple probabilities and expectations from probability density functions (pdfs)<\/li>\n<li>Likelihood ratio tests from pdfs for statistical engineering problems.<\/li>\n<li>Least -square &amp; maximum likelihood estimators for engineering problems.<\/li>\n<li>Mean and covariance functions for simple random processes.<\/li>\n<\/ul>\n<p><strong>For more information about all JNTU updates please stay connected to us on FB and don\u2019t hesitate to ask any questions in the comment.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>JNTUH B.Tech 2nd year Probability Theory and Stochastic Processes gives you detail information about Probability Theory and Stochastic Processes Engineering R13 year subject. It will be help full you to [&hellip;]<\/p>\n","protected":false},"author":2259,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[3,152,121,62],"tags":[],"class_list":["post-891","post","type-post","status-publish","format-standard","hentry","category-ece","category-1st-sem-2","category-2nd-year","category-syllabus"],"_links":{"self":[{"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/posts\/891","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/users\/2259"}],"replies":[{"embeddable":true,"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/comments?post=891"}],"version-history":[{"count":5,"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/posts\/891\/revisions"}],"predecessor-version":[{"id":17785,"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/posts\/891\/revisions\/17785"}],"wp:attachment":[{"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/media?parent=891"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/categories?post=891"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/tags?post=891"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}