# indian institute of technology rajasthan

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```INDIAN INSTITUTE OF TECHNOLOGY RAJASTHAN
(SUMMER TERM 2013-14)
Course Number
: 22001
Course Title
: Probability & Statistics
Instructor
: Dr. Gaurav Bhatnagar
UNIT 1: INTRODUCTION TO PROBABILITY
Definitions, sample, space & events, joint & conditional probability, dependent events.
Elementary theory of probability, Baye’s theorem with simple applications, Expected value.
UNIT 2: RANDOM VARIABLES
Introduction, distribution & density functions, discrete & continuous random variables, special
distributions: binominal, poisson, uniform, exponential, normal, rayleigh. Central limit theorem.
UNIT 3: EXPECTATION, CONDITIONAL DISTRIBUTION AND CONDITIONAL
EXPECTATION
Random variable, Expectation of random variable, joint distribution functions, joint probability
density function, conditional distribution & density functions, Conditional Expectation. Mean &
variance, chebyshev’s inequality, characteristic functions & moment generating function,
covariance & correlation coefficient of multiple random variables.
UNIT 4: REGRESSION, CORRELATION AND STATISTICAL INFERENCE
Introduction, Least-square curve fitting, multiple regression, Correlation Analysis, method of
maximum likelihood estimation, point estimation, Estimation of variance, Hypothesis testing.
Text Books:
 Sheldon M. Ross, Introduction to probability and statistics for engineers and scientists,
Elsevier.
 Vijay K. Rohatgi and A. K. Md. Ehsanes Saleh, An Introduction to Probability and Statistics,
Wiley.
 Kai L. Chung and F. Aitsahlia, Elementary Probability Theory, Springer.
Reference Books:
 Robert V. Hogg, Allen T. Craig and Joeseph W. McKean, Introduction to Mathematical
Statistics, Pearson.
 William Feller, Introduction to Probability theory and its applications, Wiley.
 Richard A. Johnson, Miller and Freund’s Probability and Statistics for Engineers, PHI
Learning.
 T.T. Soong, Fundamentals of Probability and Statistics for Engineers, Wiley.
Evaluation Plan:
S.No.
1.
2.
3.
4.
Title
Quiz/Attendance
First Mid-term
Second Mid-term
End Exam
Weightage
20%
20%
20%
40%
Note: No makeup exams for quizzes and mid-term exams. However, the end exam will be
considered only after submitting the proper documentation.
```