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Probability and Random Processes

Indian Institute of Technology Guwahati , NPTEL via Swayam

Description

About the course:This course aims to introduce students from a Hindi medium background to the basics of probability and random processes and is a beginner level course. Our aim is to give the students a simple, yet thorough introduction to the course in Hindi, making it easier for them to understand the basics of this course, and its applications to Electronics and Communication Engineering. During this course, we will also build a formal vocabulary and introduce the students to the English equivalents of those terms, making it easy for them to take other courses in the language of their choice.PRE-REQUISITES:Only basic calculus is requiredINTENDED AUDIENCE:BTech students with a background from Hindi medium to introduce them to the technical aspects of probability theory in Hindi. PG (Mathematics and Commerce) students of the Hindi medium distance education programs such as IGNOU and MDU Rohtak.INDUSTRY SUPPORT:Nill

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Syllabus

Week 1: यादृच्छिक परीक्षण, घटनाएं , घटनाओं का बीजगणित (Random Experiments, Events and Algebra of Events); घटना समष्टि (Event Spaces); उदाहरण (Examples) Week 2:सप्रतिबंध प्रायिकता (Conditional probability); सप्रतिबंध प्रायिकता के कुछ उदाहरण (Some Examples); बेज़ का प्रमेय (Bayes Theorem) Week 3:असंतत यादृच्छिक चर (Discrete Random Variables); असंतत यादृच्छिक चर के कुछ उदाहरण (Examples); प्रायिकता बंटन फलन एवं संचयी बंटन फलन (Probability Mass Functions and Cumulative Distribution Functions ) Week 4:कुछ विशिष्ट असंतत प्रायिकता बंटन (Some important probability distributions ); संतत यादृच्छिक चर (Continuous Random Variables); प्रायिकता घनत्व फलन (Probability Density Function) Week 5:कुछ विशिष्ट संतत यादृच्छिक चर (Some important continuous random variables ); उदाहरण (Examples); यादृच्छिक चरों के फलन (Functions of random variables) Week 6:दो यादृच्छिक चर (Two Random Variables); संयुक्त बंटन फलन (Joint distribution functions); कुछ उदाहरण (Examples) Week 7:सप्रतिबंध बंटन (Conditional Distributions); सप्रतिबंध बंटन के उदाहरण (Examples); अनेक यादृच्छिक चरों के फलन (Functions of more than one random variables) Week 8:सहसंबंध एवं सहप्रसरण (Correlation and Covariance); सप्रतिबंध प्रत्याशा (Conditional Expectation); पूर्वानुमान में सप्रतिबंध प्रत्याशा का प्रयोग (Application of Conditional Expectation in Prediction) Week 9:यादृच्छिक चरों के अनुक्रम (Sequences of Random Varibales); उदाहरण (Examples); अभिसरण (Convergence) Week 10:केन्द्रीय सीमा प्रमेय (The Central Limit Theorem); सबल वृहद संख्या नियम (The Strong Law of Large Numbers); केन्द्रीय सीमा प्रमेय के अनुप्रयोग (Applications) Week 11:यादृच्छिक प्रक्रियाओं की परिकल्पना (Description of Random Processes); कुछ असंतत उदाहरण (Discrete Examples); कुछ संतत उदाहरण (Continuous Examples) Week 12:यादृच्छिक प्रक्रियाओं के गुणधर्म (Properties of Random Processes); स्थावरता (Stationarity); उदाहरण (Examples)