Master's Thesis from the year 2019 in the subject Mathematics - Stochastics, grade: 8.5, course: Integrated MSc in Mathematics and Computing, language: English, abstract: We are interested in the behaviour of a determinant with i.i.d. random variates as its elements. A probabilistic analysis has been done for such determinants of orders 2 and 3. We have considered some of the well known distributions, namely, discrete uniform, Binomial Poisson, continuous uniform, standard normal, standard Cauchy and exponential. We are able to give fiducial limits for the determinant using Chebyshev's inequality for all the distributions discussed in the text (except standard Cauchy distribution for which expectation does not exist). The main objective is to find the probability distribution of the determinant when its elements are from any of the distributions stated above. The desired distribution has been approximated using the method of transformation in general but when this method could not produce desired results we relied on empirical results based on simulation.
Dr. Soubhik Chakraborty, an M.Sc. (Statistics), PhD (Science) and NET (UGC/CSIR) in Mathematical Sciences, is currently serving as the Professor & Head, Department of Mathematics at Birla Institute of Technology, Mesra, Ranchi, India. His research interests are algorithm analysis, music analysis and statistical computing. He has published several books, research monograms and research papers in peer reviewed journals of international and national repute in these areas apart from guiding several research scholars leading to PhD. He is also an acknowledged reviewer associated with ACM, AMS and IEEE. He has been a visiting scientist twice to Indian Statistical Institute (Bangalore Centre in 2002, Kolkata Centre in 2004, the latter under INSA fellowship). He is a leading figure in computational musicology and has written the first book on the topic (in the context of Hindustani music; see ref [1] in relevant publications). He has been the principal investigator of a UGC major research project titled Analyzing the structure and performance of Hindustani classical music through statistics in his institute. He has received several awards in both teaching and research including the National Award for Teaching Excellence (Mathematics) given by Indus Foundation (2013) and the Best Academic Researcher Award 2013 given by Association of Scientists, Developers and Faculties (2013). Prior to joining this institute in 2006 (Nov 30), he served as a lecturer in Statistics at T.M. Bhagalpur university where he taught Statistics at both undergraduate and postgraduate levels for about ten years. Relevant Publications (books): - 1.Soubhik Chakraborty, Guerino Mazzola, Swarima Tewari and Moujhuri Patra, Computational Musicology in Hindustani Music, Springer, 2014 2.Asoke Kumar Datta, Sandeep Singh Solanki, Ranjan Sengupta, Soubhik Chakraborty, Kartik Mahto, Anirban Patranabis, Signal Analysis of Hindustani Classical Music, Springer, 2017 3.Shashi Bhushan Singh, Soubhik Chakraborty, Keashav Mohan Jha, Satish Chandra, Shanti Prakash and Swarima Tewari, Music and Medicine: Healing Brain Injury through Ragas, CBH publications, 2016
