Special Mathematics Lecture

Contact:
Serge Richard (richard@math.nagoya-u.ac.jp), Rm. 247 in Sci. Bldg. A

Introduction to probability (Spring 2021)

Registration code : 0053621
Schedule : Wednesday (18:30 - 20.00) in room 207 of Science Building A and on Zoom

• Topic : Probability and stochastic processes, mainly based on the book: Probability, an introduction from Grimmett and Welsh.

• Syllabus : the pdf file

• Class dates :
  April 14, 21, 28
  May 5, 12, 19, 26
  June 2, 9, 16, 23, 30
  July 7, 14
  

• Lecture notes : The cumulative notes

• Content :
  1) Events and probabilities
  2) Discrete valued random variables
  3) Multivariate discrete distributions
  4) Probability generating function
  5) Distribution function and density function, Examples of density functions
  6) Multivariate distributions and independence
  7) Moments and moment generating functions
  8) The main limit theorems
  9) Branching processes
  10) Random walk (1D)
  11) Random process in continuous time

• Picture : May, June

• Study sessions : Are organized on an individual basis by three students. For any information, contact Duc , Hiep, Tom.

• For the evaluation, you need to submit the solutions of some exercises and/or the proofs of some statements. These submissions can take place at any time during the semester. If you have any question, contact me or Ziyu Liu.

• Student's reports :
  Probability and partitions, by Vic Austen
  Boole's inequality, by Peng Qi
  Bonferroni's inequality, by Nguyen Duc Thanh
  Matching socks, by Hoang Hiep Nguyen
  At the bus stop, by Hoang Hiep Nguyen
  Sum of independent Poisson distributions, by Guozhang Lin
  The geometric distribution has no memory !, by Guozhang Lin
  Law of subconscious statistician, by Nguyen Minh Diep
  Poisson distribution: mean and variance, by Nguyen Minh Diep
  Binomial distribution: mean and variance, by Nguyen Minh Diep
  An even number of sixes, by Shimura Koki
  De Morgan's laws, by Dillon Loh
  Linearity of expectation, by Qiuling Low
  About variance, by Qiuling Low
  Balls in 2 urns, by Hinata Yoshida
  One more formula for the expectation, by Peng Qi
  On the gamma distribution, by Matsumoto Kosuke and Nguyen Duc Thanh
  Sum of normal random variables, by Keito Masuda
  2 discrete random variables, 1 joint mass function, by Hinata Yoshida
  Estimating the population variance from a random sample, by Nguyen Duc Thanh
  Gamma function and gamma distribution, by Guozhang Lin
  Chi-square distribution, by Guozhang Lin
  Properties of the moment generating function, by Guozhang Lin
  Linear transformation of normal random variables and its statistical application, by Guozhang Lin
  Important result related to chi-square distribution and its statistical application, by Guozhang Lin
  The relation between 2 generating functions, by Hoang Hiep Nguyen and Shimura Koki
  Buffon's needle, by Shimura Koki
  Alternative form of Chebyshev's inequality and rolling of a fair dice, by Guozhang Lin
  Fair dice thrown 12000 times, by Guozhang Lin
  About Joint density functions, by Yesui Baatar and Peng Qi
  Deriving the variance for the size of the n-th generation of the branching process, by Nguyen Duc Thanh
  Variance of branching process, by Peng Qi
  A transformation of gamma distribution tends to normal, by Guozhang Lin
  Binomial - Poisson limit, by Matsumoto Kosuke
  A joint density function, by Tomoaki Kanazawa
  Playing with dice and independence, by Liu Anke and Peng Qi
  About branching processes, by Guozhang Lin
  Asymmetric random walk revisits it starting point only infinitely often with probability 1, by Guozhang Lin
  On one distribution function, by Liu Anke and Peng Qi
  Fruits, and probability generating function, by Tomoaki Kanazawa and Peng Qi
  Moment generating function of Poisson distribution, by Guozhang Lin
  
On Poisson Processes, by Guozhang Lin
Weak law of large numbers does not apply to Cauchy distribution, by Guozhang Lin
Some useful identities, by Dam Truyen Duc
Random number sampling and Box Muller transform, by Dam Truyen Duc
The moment generating functions for some distributions, by Dam Truyen Duc
Indicator functions and independence, by Dillon Loh
On the Laplace distribution, by Dillon Loh
The symmetric random walk in Z^3 is transient, by Dam Truyen Duc
On bivariate distributions, by Nguyen Minh Diep
On bivariate standard Cauchy distribution, by Dillon Loh
Density function for 3 jointly continuous random variables, by Dillon Loh
About a joint density function, by Dillon Loh and Yana AlHebri
Integer valued random variable and Gamma function, by Hinata Yoshida
On generating functions, and the negative binomial distribution, by Hinata Yoshida
On asymmetric random walk: mean and variance, by Dillon Loh
Probability in biology: the basics of inheritance, by Yana AlHebri
Probability applied to a game, by Keito Masuda
Geometric distribution and lack of memory, by Putri Gifta Desyanmi Santosa
A bivariate discrete distribution, by Yesui Baatar
Towards some common density functions, by Yesui Baatar
Applying calculus to probability, and the unsafe little brother, by Dillon Loh and Yana AlHebri
A very dangerous game, by Yana AlHebri
More word problems, by Yana AlHebri
Expectation of absolutely continuous random variables, by Yesui Baatar
About convergence in mean square, by Liu Anke