Probability Theory

Shailaja Deshmukh is a visiting faculty at the Department of Statistics, Savitribai Phule Pune University, formerly known as University of Pune, India. She retired as a Professor of Statistics from the Savitribai Phule Pune University. She has taught around twenty five different theoretical and applied courses. She worked as a visiting professor at the Department of Statistics, University of Michigan, Ann Arbor, Michigan, during 2009-10 academic year. She has served as an executive editor and as a chief editor of the Journal of Indian Statistical Association. She is an elected member of the International Statistical Institute. Her areas of interest are inference in stochastic processes, applied probability and analysis of microarray data. She has a number of research publications in various peer-reviewed journals, such as Biometrika, Journal of Multivariate Analysis, J. R. Statist. Society, Australian and New Zealand Journal of Statistics, Journal of Applied Statistics , Environmetrics, J. of Statistical Planning and Inference, Naval Research Logistics, Journal of Translational Medicine, Annals of Institute of Statistical Mathematics. She has published the following six books. (i) Microarray Data: Statistical Analysis Using R, published by Narosa in 2007, (ii) Statistics Using R, published by Narosa in 2008, (iii) Actuarial Statistics: An Introduction Using R, published by Universities Press in 2009, (iv) Multiple Decrement Models in Insurance: An Introduction Using R, published by Springer in 2012 and (v) Asymptotic Statistical Inference: An Introduction Using R, published by Springer in 2021. (vi) Stochastic Processes: An Introduction Using R", published by Springer in 2023.Akanksha Kashikar is an Assistant Professor at Savitribai Phule Pune University (formerly known as the University of Pune) since 2012, specializing in Statistics. She obtained her masters and PhD in Statistics from the same university. Her research interests include Branching Processes, Count Data Time Series, and Applied Statistics. She has taught around fifteen different theoretical and applied courses. She has published papers in various Sci/Scopus listed journals including the Journal of Statistical Planning and Inference, Statistics and Probability Letters, Annals of the Institute of Statistical Mathematics, Communication in Statistics, Environmental Science and Pollution Research, Proteome Science, Journal of Astrophysics and Astronomy etc. She has developed an R Package “Outlier Detection” which has been downloaded more than 15000 times. She is an executive editor for the Journal of Indian Statistical Association. She has received several awards, including the Young Statistician Award and the Young Scientist Award from Indian statistical societies, and the Best Paper Award from the Indian Society for Medical Statistics. She was granted a research fellowship through the Indo-Japanese Young Researcher Fellowship Programme. She is passionate about science popularization and has written articles in Marathi publications. She has also been recognized for her innovative teaching methods. (Award by SPPU)

• 1. Sigma Field, Borel Field and Probability Measure 2. Random Variables and Random Vectors 3. Distribution Function 4. Expectation and Characteristic Function 5. Independence 6. Almost Sure Convergence and Borel Zero-One Law 7. Convergence in Probability, in Law and in r-th Mean 8. Convergence of a Sequence of Expectations 9. Laws of Large Numbers 10. Central Limit Theorem 11. Solutions to Conceptual Exercises 12. Bibliography 13. Index