Probability Theory and Stochastic Processes Detailed Syllabus for B.Tech second year second sem is covered here. This gives the details about credits, number of hours and other details along with reference books for the course.<\/p>\n
The detailed syllabus for Probability Theory and Stochastic Processes B.Tech 2016-2017 (R16) \u00a0second year second sem is as follows.<\/p>\n
B.Tech. II Year II Sem. \u00a0 \u00a0L\/T\/P\/C
\nCourse Code: EI401ES \u00a0\u00a04\/0\/0\/4
\nPre-requisites: Nil.<\/p>\n
Course Objectives:<\/strong> The primary objective of this course is:<\/p>\n Course Outcomes:<\/strong> Upon completion of the subject, students will be able to compute:<\/p>\n UNIT \u2013 I\u00a0Probability:<\/strong> Probability introduced through Sets and Relative Frequency, Experiments and UNIT \u2013 II\u00a0Distribution & Density Functions:<\/strong> Distribution and Density functions and their Properties \u2013\u00a0Binomial, Poisson, Uniform, Gaussian, Exponential, Rayleigh and Conditional Distribution,\u00a0Methods of defining Conditional Event, Conditional Density, and Properties.\u00a0Operation on One Random Variable \u2013 Expectations: Introduction, Expected Value of a\u00a0Random Variable, Function of a Random Variable, Moments about the Origin, Central\u00a0Moments, Variance and Skew, Chebychev\u2019s Inequality, Characteristic Function, Moment\u00a0Generating Function, Transformations of a Random Variable: Monotonic Transformations\u00a0for a Continuous Random Variable, Non-monotonic Transformations of Continuous Random\u00a0Variable, Transformation of a Discrete Random Variable.<\/p>\n UNIT \u2013 III\u00a0Multiple Random Variables:\u00a0<\/strong>Vector Random Variables, Joint Distribution Function, Properties of Joint Distribution,\u00a0Marginal Distribution Functions, Conditional Distribution and Density \u2013 Point Conditioning,\u00a0Conditional Distribution and Density \u2013 Interval conditioning, Statistical Independence, Sum\u00a0of Two Random Variables, Sum of Several Random Variables, Central Limit Theorem (Proof\u00a0not expected), Unequal Distribution, Equal Distributions.\u00a0Operations on Multiple Random Variables:\u00a0Expected Value of a Function of Random Variables: Joint Moments about the Origin, Joint\u00a0Central Moments, Joint Characteristic Functions, Jointly Gaussian Random Variables: Two\u00a0Random Variables case, N Random Variable case, Properties, Transformations of Multiple\u00a0Random Variables, Linear Transformations of Gaussian Random Variables.<\/p>\n\n
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\nSample Spaces, Discrete and Continuous Sample Spaces, Events, Probability Definitions and\u00a0Axioms, Mathematical Model of Experiments, Probability as a Relative Frequency, Joint\u00a0Probability, Conditional Probability, Total Probability, Baye\u2019s Theorem, Independent Events.\u00a0Random Variable: Definition of a Random Variable, Conditions for a Function to be a\u00a0Random Variable, Discrete, Continuous, and Mixed Random Variables<\/p>\n