Tagged Questions
1
vote
2answers
49 views
What exactly does this physically mean?
Let X(w) be a real random variable on ($\Omega$ , P). The image X($\Omega$) the set of all the values X(w) can take ,written $\Omega^{X}$. For any set $ B \subset \Omega^{X}$ the probability of the ...
1
vote
1answer
26 views
Rademacher random variables in terms of Bernoulli
I've found out that Rademacher random variables and Bernoulli random variables plays an important role in Probability theory. I am wondering how they are connected. For example,
Let $r_i, i=1, ...
-2
votes
2answers
84 views
Is first order moving average a Markov process?
Given first order moving average
$$
x(n) = e(n) + ce(n-1)
$$
where $e(n)$ is a sequence of Gaussian random variables with zero mean and unit variance which are independent of each other, and $c$ is ...
1
vote
0answers
55 views
What's the probability of creating a Hello World Program?
Consider an application that has knowledge of all characters on the keyboard i.e. if asked to do so it can randomly choose any character and output it.
Now, in the programming language Java consider ...
4
votes
3answers
378 views
Repeating something with (1/n)th chance of success n times
Is there anything that can be said about how many attempts it will take to correctly guess a random number out of 1000 numbers? If the number wouldn't change the probability would just increase every ...
1
vote
1answer
57 views
Two sequences of random variables
Consider two sequences of random variables $X_n, Y_n$ and suppose $X_n\to X$ in distribution. Does the following hold: $\lim_{n\to\infty} E[|X_n-Y_n|]=0 \implies Y_n\to X$ in distribution?
1
vote
1answer
131 views
Is the expectation $E[\xi U'(\xi)]$ finite?
I encounter the following problem today. It seems a simple question.
Let $U$ be a real function from $R^+\rightarrow \bar{R}$ satisfying the following conditions:
(1) $U$ is concave, continuous, ...
2
votes
1answer
105 views
Image countable when state space is not?
From Jacod / Protter: "Probability Essentials", Springer:
Note that even if the state space (or range space) $T$ is not countable, the image $T'$ of $\Omega$ under $X$ (that is, all points ...
2
votes
1answer
157 views
What are the relationships between combinatorics and randomness?
I was just reading the impressive paper by Tim Gowers The Two Cultures of Mathematics when I noticed the various connections between combinatorics and randomness. As a non-mathematician, it is not ...
0
votes
2answers
74 views
Convergence of sum of independent random values
If $f(x)>0$ is any function st. $\sum_{j=1}^{\infty}f(j)=\infty$. And $a_n=f(n)$ with probability 50%, else 0.
Does $\lim_{n\rightarrow\infty}((1/\sum_{j=1}^nf(j)) \sum_{k=1}^n a_k)=1/2$ almost ...
0
votes
3answers
64 views
how much the entropy change going from 6 digit, to 8 digits with several sequence restrictions?
One system I use just changed their password policy. Previously, the only requirement was 6 digits. (e.g. 123456, 111111)
Now it's 8 digit, with no bigger then 3 digit sequence, and no pattern such ...
3
votes
4answers
315 views
Random variables: How would you explain it to a beginner?
Different types of random variables:
(discrete) Binomial, hypergeometric, geometric, Poisson
(continuous) Uniform, normal, exponential
Random variables are very useful tools when solving simple and ...
0
votes
0answers
189 views
Choosing a random natural number with bijection with rationals
It's said that you can't choose a random natural number. But what if you take a bijection between the natural numbers and, say, the rational numbers in the unit interval, and then choose a random ...
2
votes
0answers
76 views
Likelihood Function of Random Process
Given the following data:
$$
x(t) = A + \omega(t)
$$
where $ \omega(t) $ is an AWGN with zero mean, what would be likelihood function $p(x(t);A)$?
I know it could be proven to be:
$$
p(x;A) = C ...
0
votes
2answers
263 views
Calculate the probability of a simple event
I'm beginning to study probability and an exercise in the study guide that asks me to calculate: What is the probability that the month January, of one year randomly selected have only four Sundays?
...
0
votes
1answer
129 views
How to measure the amount of uncertainty
What are the possible measures of uncertainty for a discrete variable X=(x1, x2, ... xn), where values are defined by the alphabet - xi ∈ A, given probabilities p(xi) = P(X = xi) change over time?
...
3
votes
3answers
211 views
Definition of random
Suppose that you has to guess given a set of numbers
If they are random.
The mathematical expectation
Is there a definition of randomness that allow this prove/test?
Is even possible? if so: How ...
4
votes
2answers
360 views
Connection to Normal distribution
I've been working on finding the probability for the event, that the sum of $n$ independent random variables are less than $s$, when they are evenly distributed on $[0,1)$.
I've used the law of total ...
2
votes
3answers
171 views
Expected time of tree search algorithm on random input
We have a perfect binary tree on 2^k-1 nodes. Every node in the tree is marked with probability 1/2, and a node is either marked or unmarked. We want to find a marked node and return it. Our algorithm ...
1
vote
1answer
179 views
Random assignment in blind experiments and “fair / just coin”
In blind experiments subjects are randomly assigned to one of groups. The most commonly used solution is to use (equivalent of) a coin toss, with the same probability to be assigned to each group.
I ...
9
votes
1answer
135 views
How can I randomly generate trees?
I want to randomly generate trees, i.e. undirected acyclic graphs with a single root, making sure that all possible trees with a fixed number of nodes n are equally likely.
