Download Annexure `AAB-CD-01` L T P/S SW/FW TOTAL CREDIT UNITS 3 1 0

Annexure ‘AAB-CD-01’
Course Title: PROBABILITY THEORY – I
Course Code: to be decided later
Credit Units: 4
Level: UG
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Course Title
Course Objectives:
 The objective of the course is to develop knowledge of the fundamentals of the
probability theory for determining the risk and assessing the various problems
based on it.
 The application of this theory in various decision making problems especially
under uncertainties.
2 Prerequisites:
NIL
3 Student Learning Outcomes:
 The students will be able to distinguish between probability models appropriate to
different chance events and calculate probability according to these methods.
 The students will learn to get the solution of the problems based on probability
space and limit theorems.
 The students will learn to get the solution of the problems based on random
variables and distribution functions.
 The students will learn to get the solution of the problems based on mgf and cf for
discrete and continuous distributions.
 The course enables the students to develop the skill set to solve probability based
real life problems.
Course Contents / Syllabus:
4 Module I:
SW/F
W
0
Weighta
ge (%)
1
5
Random experiment, trial, sample point and sample space, events, operations of events,
concepts of equally likely, mutually exclusive and exhaustive events.
Definition of probability: Classical, relative frequency and axiomatic approaches. Discrete
probability space, properties of probability under set theoretic approach. Independence of
events, Conditional probability, total and compound probability theorems, Bayes theorem
and its applications.
Module II:
6
Random variables – discrete and continuous, probability mass function (pmf) and
probability density function (pdf), Cumulative distribution function (cdf). Joint distribution
of two random variables, marginal and conditional distributions.
Module III:
7
Independence of random variables. Expectation of a random variable (rv) and its
properties, expectation of sum of random variables and product of independent random
variables, conditional expectation and related problems.
Module IV:
25%
Weighta
ge
25%
Weighta
ge
25%
Weighta
ge
25
TOTAL
CREDIT
UNITS
4
Weighta
ge
8
9
Moments, moment generating function (m.g.f.) & their properties, continuity theorem for
m.g.f. (without proof).Chebyshev’s inequality.
Complements and problems.
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in a separate
Lab sessions. In addition to numerical applications, the real life problems and situations
will be assigned to the students and they are encouraged to get a feasible solution that
could deliver meaningful and acceptable solutions by the end users.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
70%
End Term
Examination
MidTerm
Exam
Project
Viva
Attendance
10%
10%
5%
5%
Weightage (%)
70%
Text & References:
1. Parzen, E.S. : Modern Probability Theory and its Applications.
2. Meyer, P. : Introductory Probability and Statistical Applications.
3. Stirzekar David (1994) : Elementry Probabilityu, Cambridge University Press.
4. Mood A.M., Graybill F.A. and Boes D.C. (1974) : Introduction to the theory of
Statistics, McGraw Hill.
5. Mukhopadhyay, P : Mathmatical Statistics, new central book agency.
6. Hoel, P. G., Port, S. C. and Stone, C. J, Introduction to Probability Theory, Universal Book
Stall, New Delhi, Reprint 2003.
7. Chung, K. L., A Course in Probability Theory, Academic Press, San Diego, USA, 2001
Remarks and Suggestions:
_______________________________
Date:
Name,
Designation,
Organisation