Tagged Questions
0
votes
1answer
18 views
Time Periodic Homogeneous Markov Chain
I want to find a textbook or survey article reference with a treatment of discrete-time, inhomogeneous, yet time periodic, markov chains on finite state spaces.
Elaboration: I have an inhomogeneous ...
2
votes
1answer
48 views
Any comprehensive material to revise the mathematics
I left school long back and so my mathematics knowledge also fades out.
I am trying hard to re-collect the basics about log / permutaion / combination / probability / polynomial equations.
I tried ...
0
votes
1answer
27 views
Theoretical book on Bayesian Networks
Does anyone know any concise book on Bayesian Networks and related material written for mathematicians? Most books that I know are written for the Machine Learning and AI crowd and are way too chatty ...
3
votes
1answer
151 views
source of proof for a characterization of normal distribution
I want to know the proof of the following statement about normal distribution:
If the sample mean and sample variance are independent for a population, then the distribution of the population is ...
1
vote
1answer
32 views
textbooks on probability and statistics
I want a textbook on probability and statistics that's short , concise and easy to read that's written for mathematicians and physicists . I want it for my study of statistical mechanics
1
vote
0answers
17 views
Large $k$ asymptotic of $\Pr(X=k)$ for a compound Poisson random variable $X$
Let $N \sim \operatorname{Poisson}(\mu)$, and let $X|N = \sum_{k=1}^N Y_k$, where $Y_k$ are iid non-negative integer-valued random variables. The distribution of $X$ is known as compound Poisson ...
5
votes
1answer
82 views
Measure on a separable Hilbert space
Let $H$ be a real separable Hilbert space.
Is it true that there exist a probability space $(\Omega, \mu)$ and a measurable function $\pi\colon \Omega \to H$ such that for any $h \in H$ we have
$$
...
2
votes
0answers
30 views
Comparing the mean to the standard deviation
Let $X_1,X_2, \ldots ,X_n$ be i.i.d. random variables with normal distribution
${\cal N}(\mu,\sigma)$. Let
$$
M=\frac{X_1+X_2+ \ldots +X_n}{n}, \
D=\sqrt{\sum_{k=1}^n (X_k-M)^2},\
Y=\frac{X_1+X_2+ ...
4
votes
5answers
112 views
Rigorous probability text for math major
Most probability texts that do not use measure theory seemed to be geared toward engineers and the like, while more advanced texts already assume a strong background in measure theory and Lebesgue ...
-3
votes
1answer
111 views
Reference Request: Video Lectures for Stochastic Processes
It is difficult to learn Stochastic Process by self-reading. Can you provide some video lectures on Stochastic Process?
2
votes
1answer
28 views
a random process model which I do not know the name of
My friend explained to me the following model which comes psychology. I am fairly certain there must be mathematicians who study this type of thing because on its own right it is a very interesting ...
2
votes
0answers
119 views
Boundedness of expected reward Markov chain (may be related to discret $M/M/\infty$ queue)
[EDIT]:
I read a bit on $M/M/\infty$ queue and it may not be the right comparison and my notation may be confusing (I'm in discrete time and $\lambda,\mu$ look likes rates when they are probability). ...
1
vote
1answer
149 views
What is some books at the level which including this inequality and its proof?
I always wanting to looking into harder random variable/probability/stochastic process/statistics books
that are harder than the intro one and have multiple random variable but easy enough to have ...
13
votes
1answer
156 views
Expected rank of a random binary matrix?
Recently a friend stumbled across this question:
Let $M$ be a random $n \times n$ matrix with entries in $\{0,1\}$ (both zero and one has probability $p = q = \frac{1}{2}$). What is its expected ...
7
votes
8answers
837 views
Self-study resources for basic probability?
I am taking a Computer Science class soon that requires a solid knowledge of the basics of probability. I've only had minimal exposure to probability in classes I've taken in the past, so I need to ...
