Course

Unit 1

Jointly Distributed Random Variables, Independent Random Variables, Conditional Distributions, Expectation and Variance and their properties, Expected Value of Sums of Random Variables, Variance, Variance of Sums of Random Variables, Covariance and Correlation Coefficient, Weak law of large numbers and Central limit theorem for i.i.d random variables.

Unit 2

Definitions of random sample, parameter and statistic, sampling distribution of a statistic, Sampling distribution of sample mean, Standard errors of sample mean, sample variance and Sample proportion. Exact sampling distribution χ2, student’s t distribution, Snedecore’s F-distribution and nature of p.d.f. curve with different degrees of freedom, mean and variance, Relationship between t, F and χ2 distributions.

Unit3

Parameter Estimation: Introduction, Definition of estimators, and estimates, Desirable properties of estimates, Maximum Likelihood Estimation and method of moment estimation, Interval Estimates of mean, variance and proportion.

Unit 4

Hypothesis Testing –Introduction, Significance Levels, Large sample tests for mean, equality of means and proportions, small sample tests for the mean, equality of means and variance of normal populations.
Goodness of Fit Tests and Categorical Data Analysis, Goodness of Fit tests when all parameters are Specified, Goodness of Fit Tests When Some Parameters are unspecified, Tests of Independence in Contingency Tables, Tests of Independence in Contingency Tables having fixed marginal totals.

Unit 5

Analysis of variance: Definitions of fixed, random and mixed effect models, analysis of variance and covariance in one-way classified data for fixed effect models, analysis of variance and covariance in two-way classified data with one observation per cell for fixed effect models.
Text Book:
Douglas C. Montgomery and George C. Runger, Applied Statistics and Probability for Engineers, John Wiley and Sons Inc., 2005
References:

Course Outcome:

CO1: Understand the joint distribution of random variables, marginal and conditional distributions, independence of random variables, expectation, variance, covariance and correlation of random variables.
CO2: Understand the concept of population, sample, parameter and statistic, and distributions of statistic
CO3: Able to understand the standard sampling distributions
CO4: Able to understand the statistical estimation procedures and standard methods of estimation of parameters
CO5: Ability to  understand testing of hypothesis and standard statistical tests of hypothesis.

Text Book:
Douglas C. Montgomery and George C. Runger, Applied Statistics and Probability for Engineers, John Wiley and Sons Inc., 2005

References:

1. Ross S.M., Introduction to Probability and Statistics for Engineers and Scientists, 3rd edition, Elsevier Academic Press.
2. Ravichandran, J. Probability and Statistics for engineers, First Reprint Edition, Wiley India, 2012 Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers and Keying Ye, Probability and Statistics for
3. Engineers and Scientists, 8th Edition, Pearson Education Asia, 2007
4. Hogg, R.V., Tanis, E.A. and Rao J.M., Probability and Statistical Inference, Seventh Ed, Pearson Education, New Delhi