Probability and Statistics detailed Syllabus for Cloud Computing & Big Data (BD), K scheme PDF has been taken from the MSBTE official website and presented for the diploma students. For Subject Code, Subject Name, Lectures, Tutorial, Practical/Drawing, Credits, Theory (Max & Min) Marks, Practical (Max & Min) Marks, Total Marks, and other information, do visit full semester subjects post given below.
For all other MSBTE Cloud Computing & Big Data 4th Sem K Scheme Syllabus PDF, do visit MSBTE Cloud Computing & Big Data 4th Sem K Scheme Syllabus PDF Subjects. The detailed Syllabus for probability and statistics is as follows.
Rationale
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Course Outcomes:
Students will be able to achieve & demonstrate the following COs on completion of course based learning
- Apply the basics of probability to solve the engineering problems.
- Use the concepts of random variable and types of probability distribution for getting the spread of d
- Apply network analysis to estimate the complex pattern of relationship and network structure.
- Apply the Bivariate frequency distribution and correlation for data analysis.
- Apply Regression analysis to determine the correlation of data.
Unit I
Probability 1.1 Definition and types of events :Simple event, Occurrence & non-occurrence of an event, Sure event, Impossible event, Complementary event 1.2 Algebra of events (Union, Intersection and Mutually exclusive) , Elementary Properties of Probability 1.3 Addition theorem of two event using axiomatic definition of property and using Venn diagram 1.4 Conditional probability, Multiplication theorem, Independent events 1.5 Problems on Bayes’ Theorem (without proof)
Suggested Learning Pedagogie
Improve lecture Chalk Bo Tutorial Flipped classroo
Unit II
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Unit III
Network Analysis (PERT and CPM) 3.1 Construction of Network Diagram A-O-A Network (Activity on Arrow Network), Guidelines, Fulkerson’s rule for numbering events, Interdependency, Node Relationship, Dummy activity, Common errors in Networking 3.2 Determination of Critical path: Network diagram, Paths in network 3.3 PERT Algorithm: Estimate Three kinds of time estimates in PERT, Networking diagram, Probability calculation, Expected project completion date
Suggested Learning Pedagogie
Improve lecture Chalk Bo Tutorial Flipped Classroo
Unit IV
Bivariate frequency distribution and correlation 4.1 Correlation: Definition and Types of correlation(Positive,Negative,Linear and Non linear) 4.2 Scatter diagram, Karl Pearson’s co-efficient of correlation and Spearman’s Rank co-efficient of correlation 4.3 Marginal frequency distribution, Conditional frequency distribution
Suggested Learning Pedagogie
Improve lecture Chalk Bo Tutorial Flipped Classroo
Unit V
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List of Experiments:
- Find the union, intersection and complement of events based on Venn diagram for the given problem. 1 C
- * Calculate the probability using concepts of conditional probability and Bayes theorem for the given problem. 1 C
- Find the Expected value, Variance and Standard Deviation for the given problem. 1 C
- * Calculate the probability using Bernoulli distribution for the given problem. 1 C
- *Calculate the probability using Uniform distribution for the given problem. 1 C
- Calculate the probability using Exponential distribution for the given problem. 1 C
- Construct the Network diagram (A-O-A ) Activity on Arrow network. 1 C
- Find the critical path using Fulkerson’s rule for numbering events for the given problem. 1 C
- *Calculate the Expected time using PERT algorithm for the given problem. 1 C
- * Calculate the Karl Pearson’s coefficient of correlation to the given data. 1 C
- * Calculate the Spearman’s Rank co-efficient of correlation to the given data. 1 C
- Find the Marginal frequency distribution and Conditional frequency distribution for the given problem. 1 C
- * Find the Standard deviation of data,covariance,coefficient of correlation and coefficient of regression for the given problem. 1 C
- Determine the best way of fitting the curve by least square method. 1 C
- * Find the equation to line of regression (X on Y and Y on X) for the given problem. 1 C
Self Learning
Micro Project
- Write a program to apply marginal frequency distribution of predictors and response variables.
- Collect the data of marks obtained by students in any two subjects X and Y in mid sem test .Calculate the regression equation of X on Y and regression equation of Y on X.
- Implement each least squares regression technique using a programming language such as Python or R.Util libraries like scikit -learn for implementation, ensuring proper parameter tuning and regularization settings for technique.
- Collect the data of the students of your class who like tea ,coffee and milk and prepare a Venn diagram to re the data.
- Analyze sports data and provide insights into player performance, team dynamics, and game strategies usin probability.
Assignment
- Collect 5 examples based on Spearman’s Rank Coefficient of Correlation.
- Collect examples based on real world applications of probability and prepare a pdf file.
- Collect the data of 50 students of your class to take their heights in cm(x) and weights in kg (y).Hence find the regression equation.
- Practice linear, non-linear, and directly proportional relationships with interactive resources from GeoGebra prepare a pdf file.
- Collect at least 10 examples based on real world applications of network analysis.
Other
- Complete any one course related to “Probability and Statistics” available on Coursera, Swayam, NPTEL.
Laboratory Equipment
For the complete Syllabus, results, class timetable, and many other features kindly download the iStudy App
It is a lightweight, easy to use, no images, and no pdfs platform to make students’s lives easier..
Learning Materials
- H.K. Dass , Er. Rajnish Verma Higher Engineering of Mathematics S.Chand Publication,New Delhi,2008 ISB 9788121938902
- S.C.Gupta & V.K. Kapoor Fundamental of Mathematical Statistics Sultan Chand & sons Publication,New Delhi,2008 ISBN: 978-8180545283
- Grewal B. S. Higher Engineering Mathematics Khanna publication, New Delhi, 2013. IS 978-8174091955
- Er.Prem Kumar Gupta & Dr.D.S.Hira Operation Research S.Chand Publication, New Delhi,2008 IS 978-8121902816
- Dr. J. Ravichandran Probability & Statistics for Engineers Wiley India Pvt Ltd, ISBN: 978-8126523
- Dr B.C Punmia and K.K Khandelwal Project Planning and Control with PERT and CPM Laxmi publications, ISBN :81-7008-309-
Learning Websites & Portals
- https://www.coursera.org/learn/introductiontoprobability An Intuitive Introduction to Probabil
- https://nptel.ac.in/courses/111106112 Online Learning Initiatives by IITs
- https://www.edx.org>learn>probabilty Foundational concepts of probability theory and statistics
- https://www.khanacademy.org/math/statistics-probability/prob ability-library/addition-rule-lib/a/addition-rule-for-probab ility-basic Foundational concepts of probability
- https://www.udemy.com/course/axiomatic-probability/ Understanding Axiomatic Approach Probability in Mathematics
For detail Syllabus of all other subjects of Cloud Computing & Big Data, K scheme do visit Cloud Computing & Big Data 4th Sem Syllabus for K scheme.
For all Cloud Computing & Big Data results, visit MSBTE Cloud Computing & Big Data all semester results direct links.