Tagged Questions

1
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1answer
32 views

What kind of functions can be moment-generating functions for a random variable?

Given an infinitely differentiable function $ g: \mathbb{R} \rightarrow \mathbb{R}$, can we always find a distribution function $f_X$ of some random variable $X$ so that $g(t) = \int_{-\infty}^\infty ...
0
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1answer
31 views

Post-Uni Calculus/Probabilities Book Suggestion

I have a Computer Science Background, recently graduated and I would like to refresh/improve my knowledge about probabilities and statistics (also calculus). The priority is probabilities and ...
1
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0answers
21 views

Bernstein type inequalities. Is there a standard list?

Suppose I have a sequence of iid random variables $X_i\geq 0$ with mean $\mu$ and $\mathbb E \left(e^{tX_i}\right) = G(t)$. Set $$S_n = \sum_{i=1} X_n.$$ For the purpose of this question the ...
0
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1answer
22 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
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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
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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 ...
1
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1answer
33 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
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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
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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
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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+ ...
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1answer
115 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
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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 ...
4
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5answers
114 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 ...
2
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0answers
120 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). ...
14
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1answer
157 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 ...
1
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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 ...
1
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2answers
149 views

Probability Book Help

I have Ross a First Course on Probability and Bertsekas Introduction to probability book. However these two books do not exactly give me what I am looking for. The problem is Bertsekas book is ...
0
votes
2answers
56 views

Limit case of the definition of mutual indepedence of random variable

Consider the following standard definition of mutual independence of (discrete) random variables: "A set of random variables is mutually independent iff for any finite subset $X_1, ..., X_n$ and any ...
1
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0answers
62 views

Reference for Khinchine inequality

I am looking for the proof of Khinchine inequality (see http://en.wikipedia.org/wiki/Khintchine_inequality for example), using martingales and the Azuma inequality. Can you please help me to find a ...
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0answers
78 views

Exercises for “Probability Theory: The Logic of Science: Principles and Elementary Applications”

I am learning Probability Theory: The Logic of Science, the most famous probability book. But it seems this book doesn't provide any exercises, but I do need some to test myself to see whether I ...
1
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2answers
73 views

Probability of taking balls out a bag given a series of events

Please help with me find the area to read up on to solve this type of problem: I have two bags. Bag one has 7 black marbles and 4 white marbles. Bag two has 4 black marbles and 5 white marbles. I ...
7
votes
1answer
81 views

Probability of duplicate free sample of iid discrete random sample

Let $\{X_1,\ldots,X_n\}$ be independent identically distributed discrete random variables. I am interested in computing the probability of the event that the sample is duplicate free: $$ ...
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3answers
194 views

Probability books useful for Information Theory?

Can you recommend me a list of good Probability Books for self-studying, with good explanations and introductions for Information Theory and not for the typical statistical subjects?
4
votes
3answers
357 views

Great Book on Probability and Statistics (for Computer Scientists)

I'm a Computer Science sophomore and we're studying Probability and Statistics (fundamentals and all). The teacher recommends a book which I don't like since it does not even try and explain ...
4
votes
1answer
133 views

A book of probability puzzles

I would like to train some recreational probability (Puzzles). Does any of you know a good collection? Preferably with hints or answers. I've been studying quite a bit of probability theory, but I ...
1
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3answers
65 views

Questions about assigning a probability to a randomly chosen large integer $n$ being prime

I heard this question a few days ago, so reciting from memory: If I were to randomly choose an arbitrarily large positive integer $n$, could I write a function that determines the likelihood of it ...
5
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0answers
187 views

Estimator for sum of independent and identically distributed (iid) variables

Consider the Chernoff bound described in Theorem 1 of this paper: Theorem 1. Let $X_1,\ldots,X_n$ be discrete, independent random variables such that $E[X_i] = 0$ and $|X_i|<1$ for all $i$. Let ...
1
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1answer
86 views

Marginals and compactness in the narrow topology

I've read in a working paper (bottom of page 9) that the following is a "standard result": Let $A$ be a compact metric space and $T$ be a Polish space. Let $\rho$ be a Borel probability ...
1
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1answer
60 views

Need a good reference on Levy-Ito decomposition and martingale spaces

I am currently using Appelbaum but it does not go into too much detail how we deal with the part with small jumps. Can someone please recommend a good text book? I have Bertoin at my disposal, but I ...
3
votes
0answers
23 views

Name for maximum transition probability

Let $p(x,y)$ denote the transition probability of a markov chain. Similarly, let $p^n(x,y)$ be the n-step transition probability. My question is, is there a formal name for $S(x,y):=\sup_n p^n(x,y)$. ...
1
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1answer
105 views

Good substitutes for Ross's book on Probability Models

I was wondering if there are any FREE good alternatives to Sheldon Ross's Probability Models which are more succinct? Are there any free online resources (websites/PDFs/course notes) which cover more ...
1
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0answers
60 views

Good resources for learning Probability [duplicate]

Possible Duplicate: probability textbooks I recently started taking Probabilistic Graphical Models on coursera, and 2 weeks after starting the course I am beginning to believe that I am not ...
0
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0answers
88 views

Differential Equations, Probability/Statistics, Optimization Problem - Relations?

While I am working on some physical/mathematical problems, I feel strongly that these three areas are almost the identical thing, except that they have different methods/from different aspects to ...
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0answers
92 views

derivative of conditional expectation operators $\mathbb{E}_t$?

Let $(\mathcal{F}_t)_{t\in [0,T]}$ be a filtration on a probability space $\Omega$. Fix $1<p<\infty$. Let $\{\mathcal{E}(\cdot|\mathcal{F}_t)\ :\ t\in [0,T] \}$ the associated family of ...
2
votes
0answers
115 views

Birthday paradox for non-uniform distributions

The classic birthday paradox considers all $n$ possible choices to be equally likely (i.e. every day is chosen with probability $1/n$) and once $\Omega(\sqrt{n})$ days are chosen, the probability of ...
1
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0answers
62 views

Fixed marginals of joint distribution: status

One of the well-known problems of classical probability theory is the determination of the set of all extreme points in the convex set of all probability distributions in a product Borel space $\left ...
7
votes
2answers
173 views

An extension of the birthday problem

Th birthday problem (or paradox) has been done in many way, with around a dozen thread only on math.stackexchange. The way it is expressed is usually the following: "Let us take $n$ people ...
1
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2answers
98 views

Free probability background requirements

I wish to learn free probability, and looking for a kind of program to learn it. Where should I start? Where do I continue? Which is the bibliography? and finally where do I start to learn free ...
0
votes
1answer
43 views

Introductory (online) texts on Bayesian Network.

I would like to ask for some recommendation of introductory online texts on Bayesian Network. What I am searching for is some accessible and instructive text not necessarily covering the subject in ...
3
votes
2answers
371 views

an exercise book for probability theory recommendation request

I'm looking for a good exercise book for probability theory, preferably at least partially with solutions to it. I want it to be detailed, not trivial, providing me solid fundamentals in the topic to ...
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votes
2answers
95 views

Covariance 's relationship with pure math and probabilty? [closed]

I've been looking up a lot of statistical books and cannot find out mathmatical insight behind it, but my math level wasn't allow me to read the mathmatical statistics books and get the math behind ...
3
votes
1answer
70 views

Is this a known distribution?

I came across the distribution on $(0,1]$ with the following density function $$f(x) = \frac{2}{\pi}\sqrt{\frac{1}{x}-1}$$ Is this a known distribution? Any references will be appreciated.
11
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6answers
772 views

Good books on “advanced” probabilities

what are some good books on probabilities and measure theory? I already know basic probabalities, but I'm interested in sigma-algrebas, filtrations, stopping times etc, with possibly examples of ...
0
votes
1answer
251 views

Recommendations for probability books

i do IT work, and the "it" thing these days is to throw the occasional probability question out there. The last time i stumbled on this, i'd just sat the GMAT and had probability somewhat down... ...
1
vote
1answer
102 views

random graphs without cycles

Recall that a closed walk (in a undirected graph) is a cycle if its vertices are pairwise distinct. Does there exist random constructions of bipartite graphs without cycles with high probability?
2
votes
1answer
192 views

References for Kolmogorov's strong law of a large numbers

On the Wikipedia law of large numbers site, they mention "Kolmogorov's strong law of large numbers", which works even if the random variables are not identically distributed. Where can I find this ...
0
votes
0answers
73 views

References for application of stieltjes integral in physics and prob. theory

I'd like to know riemann-stieltjes integral in area outside math. Would you help me to find some physics or math books related to application of riemann-stieltjes integral in physics about mass ...
2
votes
1answer
42 views

Probability as allocation of resources?

If we have probabilities for disjoint events: $A, B, ..., \text{i.e.:}\space P(A), P(B), ..., \text{and}\space P(A) + P(B) + \ldots = 1$ then does this in fact mean, that there is a system, that has ...
2
votes
1answer
294 views

Joint distribution of two functions of two random variables

1) Suppose I have two random variables $A > 0$ and $B > 0$ with joint p.d.f. $f_{A,B}(a,b)$, and two random variables $X = g_1(A,B)$ and $Y = g_2(A,B)$. What is the general procedure for ...
1
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1answer
130 views

Reference for probability exercises

I'm looking for challenging exercises in probability. The textbook I'm using now is Sheldon Ross's A First Course in Probability, which contains too many exercises. I don't think I have the energy to ...

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