BMS COLLEGE OF ENGINEERING, Bangalore
( Autonomous College Under VTU)
Department of Civil Engineering
M.Tech. Transportation Engineering and Management
SCHEME OF TEACHING 2018-2019
APPLIED
STATISTICS AND
PROBABILITY
COURSE OUTCOMES:
After the completion of the course students should be
Able to conceptualize and identify real world events as a function of discrete/continuous
distributions and characterize them using parameters like moments, PDF and CDF.
Able to study relationships between various factors using Regression analysis and test the
validity of these relationships using statistical decision making tools like hypothesis testing.
Unit 1
Fundamentals of probability: Classification of data – Nominal, ordinal, interval ratio,
count, Mean, variance, skewness, kurtosis, Graphical description – area, pie, bar, line, scatter
charts, Boxplots – quartiles and percentiles. Random experiments, Sample space, events,
Concepts of probability, Axioms of probability, important theorems on probability.
Unit 2
Random variables: Discrete and continuous random variables, Probability Mass Function,
Probability Density Function and Cumulative Density Function, Conditional, marginal and
joint probability, Bayer’s rule, Combinatorial analysis.
Unit 3
Types of distributions: Discrete distributions – Bernoulli, binomial, multinomial, geometric,
negative binomial, Poisson distribution, Continuous distributions – uniform, Exponential,
Gamma, normal distributions. Functions of random variables, random variable generation –
discrete and continuous using Monte Carlo method.
Unit 4
Hypothesis testing: Principle of hypothesis testing, Sample and population, Confidence
interval, level of significance, Power of a test, Central limit theorem, One-sample tests –
Mean test and variance test, Type-I & II errors, Two-sample tests – Independent and paired
sample tests, test for correlation, Test for distributions – Chi-squared test, KS or AD test.
Unit 5
Regression: Simple linear regression models, multiple linear regression models –
Interpretation of coefficients, F-test for overall goodness-of-fit of the model, assumptions in
linear regression model, and Regression F tests for comparison of models.
REFERENCES:
Bilal M. Ayyub. Richard H. McCuen. Probability, Statistics, and reliability for Engineers and
Scientists. CRC Press. Taylor and Francis Group, 3
rd
edition.