Distribution of 0 and 1 in the highest level of primitive sequences ...

The scaled sum of a sequence of i.i.d. random variables with finite positive variance converges in distribution to the normal distribution. Generalizations ...

Further results on the distinctness of binary sequences derived from ...

... primitive sequences of order 1 generated by x 5 over Z=(21). It can be seen ... Qi, “Uniqueness of the distribution of zeroes of primitive level sequences ...

arXiv:2402.11884v2 [math.NT] 10 Apr 2024

We show that if such an arithmetic sequence has level of distribution 1 the large prime factors of u tend to a Poisson-Dirichlet pro- cess, ...

Further Result on Distribution Properties of Compressing ...

In particular, the result is also true for the highest level sequence $\underline{a}_{e-1}$ by taking $\eta (x_{0},\ldots,x_{e-2})=0$. Cited By. View all.

Distribution of maximum of partial sums of independent random ...

... S0=s the maximum will not exceed the zero level, i.e. just put m=0 in (∗). How can you calculate now vn+1(s)? So you start from ...

Uniform distribution of sequences of integers - Numdam

of composite integers is uniformly distributed. For any irrational number 0 the sequence obtained by taking the integer parts of the multiples of 0, is ...

Distribution of primitive roots, as p varies - MathOverflow

Let me adjust your quantity slightly as ˜Dp(f):=1ϕ(p−1)∑x∈Φ(p)f(xp),. and let me initially impose the natural condition f(0)=f(1).

ON THE MAXIMUM PARTIAL SUMS OF SEQUENCES OF ...

... distribution function with mean 0 and variance B), ... (44) ї„ = 0((lg s„)-e) . Proof. From (6) it follows that. Page 11. 1948]. SEQUENCES OF INDEPENDENT RANDOM ...

[Q] Is it less likely for a random sequence of numbers to be 1,2,3,4,5 ...

Yes, I'm talking about uniform distribution. Our primitive intuitions may tell us that 1, 2, 3 is rarer than 78, 77, 63 [Google's random number ...

Higher-order dangers and precisely constructed taxa in models of ...

In Theorem 2, we construct a binary normal sequence that satisfies the LIL yet exhibits pairwise (two-block) bias; i.e., for any initial segment, the frequency ...

Prime number theorem - Wikipedia

This means that for large enough N, the probability that a random integer not greater than N is prime is very close to 1 / log(N). Consequently, a random ...

A proof of the Erdős primitive set conjecture | Forum of Mathematics, Pi

The study of primitive sets emerged in the 1930s as a generalization of one special problem. A classical theorem of Davenport asserts that the ...

14.4: The Poisson Distribution - Statistics LibreTexts

... most insight is a probabilistic proof based on the Poisson process. Thus suppose that N=(Nt:t≥0) is a Poisson counting process with rate 1.

On the Maximum Partial Sums of Sequences of Independent ... - jstor

(6) max 1-Bf 0 (Sn. 1_v_n where 6 is a fixed but arbitrarily small positive ... where 17,*(x) is the normal distribution function with mean 0 and variance B',.

Fast Primitive Distribution for Illustration

probability /1 0 a12 I/xi3j 1. This secondary orientation can either be a ... Decoupling strokes and high-level attributes for interactive traditional drawing.

Standard Normal Distribution - Z-Score, Area and Examples - BYJU'S

In other words, a normal distribution with a mean 0 and standard deviation of 1 is called the standard normal distribution. Also, the standard normal ...

4. Special Distributions - Random Services

Usually the standard distributions will be mathematically simplest, and often other members of the family can be constructed from the standard distributions by ...

A proof of the Erdős primitive set conjecture

99999973 ··· within P. 4Namely, the sequence of numbers 𝛾n > 0 such that 𝜁 ( 1. 2 + i𝛾n) = 0 is linearly independent over ...

Commonly Used Distributions • Random number generation ...

N(0,1) = unit normal distribution or standard normal distribution. • Key characteristics: 1. Parameters: µ = Mean σ = Standard deviation σ > 0. 2. Range ...

Uniform distribution of primes having a prescribed primitive root

From [4, Theorem 8.3] it follows that, under GRH, δ(Q(ζf ),g). = 0 if and only if either (f,h) > 1 or ∆|f. Notice that this is an easy con- sequence of Theorem ...