Tagged Questions

2
votes
1answer
38 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 $(x+y)/2$. ...
-1
votes
0answers
20 views

Random process x(t) =C and C is uniform over [-2,3]

I need reassurance that if I do a a few sample realizations of this random process they are all going to look the same. They are going to be an horizontal line with x(t) constant equal to 1/5. I see ...
2
votes
1answer
79 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 ...
0
votes
0answers
24 views

Generating sequences with specific characteristics

We are all familiar with pseudo-random sequences generated by various methods (BBS, Mersenne Twister, LCG, Von Neumann's middle square, RC4) and also the 'pseudo-random' sequence of powers of a ...
7
votes
2answers
254 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
36 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
161 views

How to check that a sequence of numbers is random?

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
49 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
158 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
97 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
181 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
88 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 ...