510904: PROBABILITY AND STATISTICS
Teaching Scheme: Examination Scheme:
Lectures: 4 Hrs/Week Theory: 70 Marks
Objectives:
To provide an introduction to probability and statistics
UNIT 1: Introduction
Interpretation of probability, sample space and events, permutations and combinations,
permutations of indistinguishable objects, Binomial Theorem, Multinomial Theorem,
Axioms of probability, conditional probability, Multiplication Rule, Bayes’ Theorem,
UNIT 2: Discrete Distributions
Random Variables, Discrete probability densities, cumulative Distribution, mathematical
Expectations, Mean, Variance, Standard Deviation, Moment Generating Function,
Geometric Distribution, Binomial Distribution, Negative Binomial Distribution, Hyper
Geometric Distribution, Poisson Distribution.
UNIT 3: Continuous Distributions
Continuous Random Variable and Probability Density, Cumulative Distribution,
Expected Value, Mean and Variance, Uniform Distribution, Gamma Function, Gamma
Distribution, Exponential Distribution, Chi-squared Distribution, Normal Distribution,
Standard normal Distribution, Weibull Distribution and reliability, Reliability of series
and parallel systems, Joint Distributions, Joint Density and Marginal Density (Discrete
and Continuous), Independence, Expectation and Covariance, Correlation, Conditional
Densities and Regression.
UNIT 4:
Descriptive Statistics: Random Sampling, Sample Statistics, Location Statistics,
measures of Variability.
Estimation: Point Estimation, Methods of moments and maximum likelihood estimation,
Functions of random Variables -Distribution of sample mean, Internal Estimation,
Confidence Interval on the mean with Variance known, Central Limit Theorem.
UNIT 5:
Interval Estimation of Variability, Estimating the Mean and Student-t Distribution,
Hypothesis Testing, Significance Testing, Hypothesis and Significance Tests on the
Mean.
Inference on proportions: Estimating proportions ,Confidence interval on p, Sample
size for estimating p, Testing Hypothesis on a proportion, Comparing two Proportions-
Estimation and Hypothesis Testing
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UNIT 6:
Categorical Data: Multinomial Distribution, Chi-squared Goodness of Fit Tests, Testing
for independence: r * c Test for Independence, Comparing proportions: r * c Test for
homogeneity
Statistical Quality Control: Properties of control charts, Shewhart control charts:
Sample Mean chart, R chart, P chart, C charts
Acceptance Sampling, Two-Stage acceptance sampling
Text Books:
1. Trivedi K., “Probability and Statistics with reliability, Queuing, and Computer Science
Applications”, PHI, ISBN: 81-203-0508-6
2. Spiegel, Schiller, “Probability and Statistics” 2nd Edition, TMH, ISBN: 0-07-058610-1
Reference Books:
1. Papoulis, Pillai, “Probability, Random Variables and Stochastic Processes”, 4th Edition,
TMH, ISBN: 0-07-048658-1
Reference http://www.unipune.ernet.in/stud_info/Syllabi/Syllabus_2008.html
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