Probability Theory: An Introduction Using R

本書介紹了使用 R 軟體的機率論，並通過結合理論與計算，以簡單易懂的方式解釋抽象概念。書中詳細討論了概念性和計算性範例，以提供對基本技術的透徹理解，並為尋求適合自學材料的學生提供愉快的閱讀體驗。內容涵蓋了基本概念，包括域、σ-域、隨機變數及其期望、隨機變數序列的各種收斂模式、大數法則和中心極限定理。

- 每章均包含基於 R 軟體的計算練習
- 包含 R 軟體基本功能的簡要介紹，適合 R 的初學者，並作為隨手參考
- 包含數值計算、模擬研究和使用 R 軟體的可視化，作為解釋抽象概念的簡易工具
- 提供多選題以供練習
- 每章均包含自我解釋的 R 代碼

本教科書適合進階學生、專業人士及統計學、生物統計學、經濟學和數學的學術研究者。

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)

Shailaja Deshmukh 是印度薩維特里拜·普赫爾大學（前身為普納大學）統計系的訪問教授。她曾擔任該大學的統計學教授並已退休。她教授過約二十五門不同的理論和應用課程。在2009-10學年期間，她曾擔任密西根大學安娜堡校區統計系的訪問教授。她曾擔任《印度統計協會期刊》的執行編輯和主編。她是國際統計學會的當選成員。她的研究興趣包括隨機過程中的推斷、應用概率及微陣列數據分析。她在多個同行評審的期刊上發表了多篇研究論文，如 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。她出版了以下六本書：(i) Microarray Data: Statistical Analysis Using R，於2007年由Narosa出版，(ii) Statistics Using R，於2008年由Narosa出版，(iii) Actuarial Statistics: An Introduction Using R，於2009年由Universities Press出版，(iv) Multiple Decrement Models in Insurance: An Introduction Using R，於2012年由Springer出版，(v) Asymptotic Statistical Inference: An Introduction Using R，於2021年由Springer出版，(vi) Stochastic Processes: An Introduction Using R，於2023年由Springer出版。

Akanksha Kashikar 自2012年以來擔任薩維特里拜·普赫爾大學（前身為普納大學）的助理教授，專攻統計學。她在同一所大學獲得了統計學的碩士和博士學位。她的研究興趣包括分支過程、計數數據時間序列和應用統計。她教授過約十五門不同的理論和應用課程。她在多個 Sci/Scopus 列名的期刊上發表了論文，包括《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》等。她開發了一個名為 "Outlier Detection" 的 R 套件，已被下載超過15000次。她是《印度統計協會期刊》的執行編輯。她獲得了多個獎項，包括印度統計學會的青年統計學家獎和青年科學家獎，以及印度醫學統計學會的最佳論文獎。她通過印日青年研究者獎學金計劃獲得了研究獎學金。她熱衷於科學普及，並在馬拉地語出版物上撰寫文章。她的創新教學方法也得到了認可（由 SPPU 頒發的獎項）。