0
votes
0answers
11 views

How do you count a grouping without a sequential count?

So, rather than explaining how this problem pertains to the actual situation I think its easier and a great deal less work to give you a situation that you can visualize. Imagine a person who has ...
1
vote
0answers
31 views

Understanding Sobol sequences

Can someone explain to me in simple terms, how Sobol sequences work? The wikipedia article is fairly technical. They look pretty interesting. So I shall describe (whatever little I know) in short the ...
0
votes
0answers
25 views

mean square convergence vs almost sure convergence

I saw a few examples that show that almost sure convergence doesn't imply convergence in mean square. Can anyone find an example of a random series that converges in mean square but doesn't converge ...
3
votes
4answers
149 views

Does this sum converge or diverge?

Does the infinite sum $\large{\sum_{n=1}^\infty \frac{1}{n^{x_{\small{n}}}}}$ converge if $x_n$ is a random variable (generated within each term) that takes values between $0$ and $2$ with equal ...
2
votes
0answers
62 views

Random walk with $\sum_{n=1}^{\infty} \frac{1}{n} \mathbb{P}\{ S_n > 0 \} < \infty$

Consider a random walk started at $S_0=0$, denoted $S_n = \sum_{k=1}^{n}X_k$, where $X_1$, $X_2$... are the i.i.d increments. If we have $\sum_{n=1}^{\infty} \frac{1}{n} \mathbb{P}\{ S_n > 0 \} ...
1
vote
0answers
49 views

determining the next random number pseudorandom number generator?

I have given 3 numbers let's say basic example x_0=5, x_1=6 and x_2=2 and modulus p is 7, ...
0
votes
1answer
96 views

Frequency analysis/discrete uniform distribution in multiple choice tests

I may be using the wrong terms in the title but I read that if something is random then each character will occur an equal amounts of times. I read this when reading about the One-Time Pad cipher, ...
0
votes
2answers
48 views

What is the statistical difference (if any) between these two methods of generating an n-digit random number?

To preface, this question is coming from a software developer so it's written from that perspective. If I need to generate a random number with $n$ digits, I could do it in one of two ways. a. Ask a ...
2
votes
1answer
52 views

Independent sequences

Let $\{x_i\}_{i = 1, ...,n}$ , $\{y_i\}_{i = 1, ...,n}$ be sequences generated by a pseudo-random number generator using different seed keys, for example $ x_0$ and $y_0$. Are $\{x_i\}$ and $\{y_i\}$ ...
0
votes
1answer
61 views

Expected length of the “greedy” increasing sub-sequence?

Given a sequence of random unique integers of length $n$, if I select every element that is the largest so far how how many elements should I expect to select? This seems superficially similar to ...
3
votes
1answer
305 views

Number of samples to predict the next number in a pseudorandom number generator

Let: $$R_{n+1} = (mR_n + b) \bmod{a} $$ Assume we know the values of $R_1, R_2, \ldots, R_L $. What is the minimum value of $L$ (if it exists) such that we can determine $R_0, m, b$ and $a$?
7
votes
4answers
1k views

Are irrational numbers completely random?

As far as I know the decimal numbers in any irrational appear randomly showing no pattern. Hence it may not be possible to predict the $n^{th}$ decimal point without any calculations. So I was ...
0
votes
1answer
44 views

How to generate sequence like this?

Can you tell what algorithm can generate sequence $x_1, x_2, x_3, x_4, ...$ satisfying: $x_n$ is real, and always $0<x_n<1$. Every change between $x_n$ and $x_{n+1}$, such as increase or ...
0
votes
1answer
87 views

When is an infinite sequence of integers purely deterministic with no randomness involved?

I see in literature very different descriptions of what is a deterministic system such as: "... a system in which no randomness is involved in the development of future states of the system...>>>" I ...
2
votes
1answer
194 views

Pick the highest of two (or $n$) independent uniformly distributed random numbers - average value?

With "random number" I mean an independent uniformly distributed random number. One Picking one random number is easy: When I pick a random number from $x$ to $y$, the average value is $(x+y)/2$. ...
2
votes
1answer
115 views

Random infinite binary sequence

What I mean by random infinite binary sequence is an infinite sequence of $0$'s and $1$'s with probability of occurrence in this sequence equal to $1/2$ (all digits being equally likely). How is it ...
7
votes
2answers
509 views

Probability that a sequence repeats itself

Given an infinite sequence $a_n$ of uniformly random integers $0$ to $9$, what is the probability there exist an integer $m$ such that the sequence $a_1$ to $a_m$ is equal to that from $a_{m+1}$ to ...
1
vote
1answer
44 views

Regularity in normal numbers

Define $f(m,n,x)$ such; let $a_j$ be the $j$'th digit in the decimal expansion of x, then $f(m,n,x)=0.a_ma_{m+n}a_{m+2n}a_{m+3n}...$ Then, if $x$ is normal, is there for every computable number ...
0
votes
2answers
260 views

How to check that a sequence of numbers is random? [duplicate]

I have a sequence of numbers like 1,7,22,45,12,96,21,45,65,36,85,14,51,16,18,17,16....65... IS there any formula to check whether the sequence is random or not ? In my case odd numbers are ...
0
votes
2answers
54 views

Given a random sequence of input points does it always produce a random output, excluding f(x) = constant?

Assume I have $y = f(x) \ne \mathrm{constant} $ and $(x_1 , \ldots ,x_N)$ a sequence N random input points, is there a set of criteria or a theorem that tells me that the output sequence $(y_1, ...
1
vote
1answer
285 views

How many 2-card swaps until a “card deck” is close to true random?

Let's define a "card deck" as a sequence of the first $x$ natural numbers, and a "swap" as the creation of a new sequence where the $i$th and $j$th member of the original sequence are exchanged e.g. ...
3
votes
2answers
103 views

Existence of a normal computable infinite pseudorandom sequence

Is there any computable infinite pseudorandom sequence of 0's and 1's which have been proven to be normal?
4
votes
2answers
243 views

Does an infinite random sequence contain all finite sequences?

If we have a finite alphabet, with each letter having a non-zero probability of being selected, will an infinite sequence of letters selected from that alphabet contain all finite sequences of letters ...
2
votes
2answers
100 views

One person's long number sequence: is it always pseudo random?

Nice to see you! I heard that computers cannot make real random sequences but only pseudorandom sequences. Is making random sequence that hard? Why? If pattern was found, changing a digit not ...