Special Mathematics Lecture
Contact:
Serge Richard (richard@math.nagoyau.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.

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

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

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
Chisquare 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 chisquare 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 nth 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
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