binomial sampling plan - meaning and definition. What is binomial sampling plan
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What (who) is binomial sampling plan - definition

TAYLOR SERIES
Newton's binomial series; Newton binomial; Newton's binomial; Newton binomial theorem

Gaussian binomial coefficient         
FAMILY OF POLYNOMIALS
Q-binomial coefficient; Q-binomial; Gaussian coefficient; Gaussian binomial; Q-binomial theorem; Gaussian polynomial; Gaussian polynomials; Gaussian binomial coefficients; Q-binomial coefficients
In mathematics, the Gaussian binomial coefficients (also called Gaussian coefficients, Gaussian polynomials, or q-binomial coefficients) are q-analogs of the binomial coefficients. The Gaussian binomial coefficient, written as \binom nk_q or \begin{bmatrix}n\\ k\end{bmatrix}_q, is a polynomial in q with integer coefficients, whose value when q is set to a prime power counts the number of subspaces of dimension k in a vector space of dimension n over a finite field with q elements.
https://en.wikipedia.org/wiki/Gaussian_binomial_coefficient
Snowball sampling         
NONPROBABILITY SAMPLING TECHNIQUE
Snowball sample; Respondent-driven sampling; Snowball method; Snowballed sample
In sociology and statistics research, snowball sampling (or chain sampling, chain-referral sampling, referral sampling (accessed 8 May 2011).Snowball Sampling, Changing Minds.
https://en.wikipedia.org/wiki/Snowball_sampling
Nyquist Theorem         
  • the sampled sequences are identical}}, even though the original continuous pre-sampled functions are not. If these were audio signals, <math>x(t)</math> and <math>x_A(t)</math> might not sound the same. But their samples (taken at rate ''f''<sub>s</sub>) are identical and would lead to identical reproduced sounds; thus ''x''<sub>A</sub>(''t'') is an alias of ''x''(''t'') at this sample rate.
  • The samples of two sine waves can be identical when at least one of them is at a frequency above half the sample rate.
  • A family of sinusoids at the critical frequency, all having the same sample sequences of alternating +1 and –1. That is, they all are aliases of each other, even though their frequency is not above half the sample rate.
  • Properly sampled image
  • Subsampled image showing a [[Moiré pattern]]
  • The figure on the left shows a function (in gray/black) being sampled and reconstructed (in gold) at steadily increasing sample-densities, while the figure on the right shows the frequency spectrum of the gray/black function, which does not change. The highest frequency in the spectrum is ½ the width of the entire spectrum. The width of the steadily-increasing pink shading is equal to the sample-rate. When it encompasses the entire frequency spectrum it is twice as large as the highest frequency, and that is when the reconstructed waveform matches the sampled one.
  • Spectrum, ''X<sub>s</sub>''(''f''), of a properly sampled bandlimited signal (blue) and the adjacent DTFT images (green) that do not overlap. A ''brick-wall'' low-pass filter, ''H''(''f''), removes the images, leaves the original spectrum, ''X''(''f''), and recovers the original signal from its samples.
  • x}}.
THEOREM
Nyquist theorem; Shannon sampling theorem; Nyquist sampling theorem; Nyquist's theorem; Shannon-Nyquist sampling theorem; Nyquist-Shannon Sampling Theorem; Nyqvist-Shannon sampling theorem; Sampling theorem; Nyquist Sampling Theorem; Nyquist-Shannon sampling theorem; Nyquist–Shannon theorem; Nyquist–Shannon Theorem; Nyquist Theorem; Shannon-Nyquist theorem; Nyquist sampling; Nyquist's law; Nyquist law; Coherent sampling; Nyqvist limit; Raabe condition; Nyquist-Shannon Theorem; Nyquist-Shannon theorem; Nyquist noise theorem; Shannon–Nyquist theorem; Kotelnikov-Shannon theorem; Kotelnikov–Shannon theorem; Nyquist-Shannon; Kotelnikov theorem; Nyquist's sampling theorem; Sampling Theorem; Nyquist Shannon theorem; Nyquist–Shannon–Kotelnikov sampling theorem; Whittaker–Shannon–Kotelnikov sampling theorem; Whittaker–Nyquist–Kotelnikov–Shannon sampling theorem; Nyquist-Shannon-Kotelnikov sampling theorem; Whittaker-Shannon-Kotelnikov sampling theorem; Whittaker-Nyquist-Kotelnikov-Shannon sampling theorem; Cardinal theorem of interpolation; WKS sampling theorem; Whittaker–Kotelnikow–Shannon sampling theorem; Whittaker-Kotelnikow-Shannon sampling theorem; Nyquist–Shannon–Kotelnikov; Whittaker–Shannon–Kotelnikov; Whittaker–Nyquist–Kotelnikov–Shannon; Nyquist-Shannon-Kotelnikov; Whittaker-Shannon-Kotelnikov; Whittaker-Nyquist-Kotelnikov-Shannon; Whittaker–Shannon sampling theorem; Whittaker–Nyquist–Shannon sampling theorem; Whittaker-Nyquist-Shannon sampling theorem; Whittaker-Shannon sampling theorem
<communications> A theorem stating that when an analogue waveform is digitised, only the frequencies in the waveform below half the sampling frequency will be recorded. In order to reconstruct (interpolate) a signal from a sequence of samples, sufficient samples must be recorded to capture the peaks and troughs of the original waveform. If a waveform is sampled at less than twice its frequency the reconstructed waveform will effectively contribute only noise. This phenomenon is called "aliasing" (the high frequencies are "under an alias"). This is why the best digital audio is sampled at 44,000 Hz - twice the average upper limit of human hearing. The Nyquist Theorem is not specific to digitised signals (represented by discrete amplitude levels) but applies to any sampled signal (represented by discrete time values), not just sound. {Nyquist (http://geocities.com/bioelectrochemistry/nyquist.htm)} (the man, somewhat inaccurate). (2003-10-21)

Wikipedia

Binomial series

In mathematics, the binomial series is a generalization of the polynomial that comes from a binomial formula expression like ( 1 + x ) n {\displaystyle (1+x)^{n}} for a nonnegative integer n {\displaystyle n} . Specifically, the binomial series is the Taylor series for the function f ( x ) = ( 1 + x ) α {\displaystyle f(x)=(1+x)^{\alpha }} centered at x = 0 {\displaystyle x=0} , where α ∈ C {\displaystyle \alpha \in \mathbb {C} } and | x | < 1 {\displaystyle |x|<1} . Explicitly,

where the power series on the right-hand side of (1) is expressed in terms of the (generalized) binomial coefficients

( α k ) := α ( α − 1 ) ( α − 2 ) ⋯ ( α − k + 1 ) k ! . {\displaystyle {\binom {\alpha }{k}}:={\frac {\alpha (\alpha -1)(\alpha -2)\cdots (\alpha -k+1)}{k!}}.}
https://en.wikipedia.org/wiki/Binomial series
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