For the family is the simplest example of just such a unit, composed of people, which gives us both some immunity from, and a way of dealing with, other people.

For example, suppose a man wearing a $200 watch, driving a 1959 Rolls Royce, stops to ask a man on the sidewalk, `` What time is it ''??

For example, there are persons who are in physical science, in the field of mineralogy, trained in crystallography, who use only X-rays, applying only the powder technique of X-ray diffraction, to clay minerals only, and who have spent the last fifteen years concentrating on the montmorillonites ; ;

For example, No. 56 printed the patent giving the Electoral Prince the title of Duke of Cambridge.

For example, he captured some persons from York County, who with teams were taking to Philadelphia the furniture of a man who had just been released from prison through the efforts of his wife, and who apparently was helpless to prevent the theft of his household goods.

For example, even the most successful executive lives in a two-room apartment while ordinary people rent space in the stairwells of office buildings in which to sleep at night ; ;

For example, in the third chapter of Matthew, verses 13-16, describing the baptism of Jesus, the 1611 version reads:

For example: 1.

For example, it probably will be necessary for the Corps to have authority to pay medical expenses of volunteers.

For example, the importance of the Regulus 2, a very promising aerodynamic ship-to-surface missile designed to be launched by surfaced submarines, was greatly diminished by the successful acceleration of the much more advanced Polaris ballistic missile launched by submerged submarines.

For example, the interest of past members of the Foundation's Advisory Board remains such that they place their knowledge and judgments at our disposal much as they had done when they were, formally, members of that Board.

For example, out of the social evils of the English industrial revolution came the novels of Charles Dickens ; ;

For example, a 12-to-one engine would power a supersonic VTOL fighter.

For example: Af.

For example: Af.

For example, for the problem Af, 10 from 25 equals 15, then 6 from 15 equals 9.

For example: Af.

For example, let's consider a standard 283 cubic inch Chevy Aj.

For an example let's dream up an engine that has a final combustion chamber volume of 5 cubic inches and a cylinder volume of 45 cubic inches.

For example, a Browning trap version of the Superposed over/under, the Broadway ( from $350 up, depending on grade ), differs from standard models in that it is equipped with a full beavertail fore end, a cushion recoil pad and a barrel-wide ventilated rib for fast sighting.

For example, the Chamber of Commerce of Gatlinburg, Tennessee, sponsors special camera tours into the Great Smoky Mountains to get pictures of the profusion of wild flowers flourishing in these wooded regions.

For example, the Friday after Thanksgiving can be substituted for Washington's birthday.

For example, the officials of Poughkeepsie town ( township ) where the project is located think highly of it because it simplifies their snow clearing problem.

For example, don't pay in a truck policy for medical coverage that you may be paying for in a health and accident policy.

For example: If your bodily injury claims start payment after the first $250, a 25% premium saving is often made.

For a Gaussian response system ( or a simple RC roll off ), the rise time is approximated by:

For general matrices, Gaussian elimination is usually considered to be stable in practice if you use partial pivoting as described below, even though there are examples for which it is unstable.

For example, if one assumes that data arise from a univariate Gaussian distribution, then one has assumed a Gaussian model:.

For example, a mixture of Gaussians with one Gaussian at each data point is dense is the space of distributions.

For example, a common choice for A < sub > o </ sub > is a Gaussian wave packet:

For example, a Gaussian wavefunction ψ might take the form:

For an ideal single-mode Gaussian beam, the D4σ, D86 and 1 / e < sup > 2 </ sup > width measurements would give the same value.

For both families, the lowest-order solution describes a Gaussian beam, while higher-order solutions describe higher-order transverse modes in an optical resonator.

For a Gaussian beam propagating in free space, the spot size ( radius ) w ( z ) will be at a minimum value w < sub > 0 </ sub > at one place along the beam axis, known as the beam waist.

For a Gaussian beam, the BPP is the product of the beam's divergence and waist size.

For a Gaussian intensity ( i. e. power density, W / m < sup > 2 </ sup >) distribution in a single-mode optical fiber, the mode field diameter is that at which the electric and magnetic field strengths are reduced to 1 / e of their maximum values, i. e., the diameter at which power density is reduced to 1 / e < sup > 2 </ sup > of the maximum power density, because the power density is proportional to the square of the field strength.

For large numbers the Poisson distribution approaches a normal distribution, typically making shot noise in actual observations indistinguishable from true Gaussian noise except when the elementary events ( photons, electrons, etc.

For example, the inverse of cumulative Gaussian distribution

For sufficiently nice prior probabilities, the Bernstein-von Mises theorem gives that in the limit of infinite trials and the posterior converges to a Gaussian distribution independent of the initial prior under some conditions firstly outlined and rigorously proven by Joseph Leo Doob in 1948, namely if the random variable in consideration has a finite probability space.

For any affine transformation of the Gaussian plane, z mapping to a z + b, a ≠ 0, a triangle is transformed but does not change its shape.

For a Gaussian distribution this is the best unbiased estimator ( that is, it has the lowest MSE among all unbiased estimators ), but not, say, for a uniform distribution.

For a Gaussian distribution, where, this means the MSE is minimized when dividing the sum by, whereas for a Bernoulli distribution with p = 1 / 2 ( a coin flip ),, the MSE is minimized for.

For example, for a laser producing pulses with a Gaussian temporal shape, the minimum possible pulse duration Δt is given by

For the HeNe laser with a 1. 5 GHz spectral width, the shortest Gaussian pulse consistent with this spectral width would be around 300 picoseconds ; for the 128 THz bandwidth Ti: sapphire laser, this spectral width would be only 3. 4 femtoseconds.

For large α, the shape of the Kaiser window ( in both time and frequency domain ) tends to a Gaussian curve.

For the Gaussian random approximation, the structure function of Tatarski ( 1961 ) can be described in terms

* For an orthogonal parametrization ( i. e., ), Gaussian curvature is:

* For a surface described as graph of a function, Gaussian curvature is: