Then again, no spam filter is 100 % immune to false positives, and the same potential correspondent that would have been deterred by address munging may instead end up wasting time on long letters that will merely disappear in junk mail folders.

Then the probability density function f *( x ) of the size biased population is

Then the probability of the measurement outcome lying in an interval B of R is | E < sub > A </ sub >( B ) ψ |< sup > 2 </ sup >.

Then the probability of a measurement returning the value λ < sub > i </ sub > can be calculated by integrating the spectral measure

Then ( Ω, F, P ) is a probability space, with sample space Ω, event space F and probability measure P.

Then the number of particles passing perpendicularly through unit area of a cross-section per unit time is the probability flux ;

Then the probability of getting this observation ( of being in interval j ) is approximately

Then has probability density function.

Let be the mean of the values in associated with class c, and let be the variance of the values in associated with class c. Then, the probability of some value given a class,, can be computed by plugging into the equation for a Normal distribution parameterized by and.

Then the probability of failure is given by

Then they are independent, but not necessarily identically distributed, and their joint probability distribution is given by the Bapat – Beg theorem.

Then, the burden shifts to the plaintiff, to affirmatively present evidence to show that they have a reasonable probability of prevailing on the action.

Then there is some probability distribution m on the interval and some random variable Y such that

Then with probability 1:

Then the theory is invariant under the Poincaré group if for every ray Ψ of the Hilbert space and every group element ( a, L ) is given a transformed ray Ψ ( a, L ) and the transition probability is unchanged by the transformation:

Then the phase space distribution determines the probability that the system will be found in the infinitesimal phase space volume.

Then the probability density function for is given by

Then the Wishart distribution is the probability distribution of the p × p random matrix

Then, if n ≥ p, has a Wishart distribution with n degrees of freedom if it has a probability density function given by

Then the conditional probability given is a function such that is the conditional expectation of the indicator function for A:

Then μ is a probability measure on the σ-algebra of Borel subsets of I.

Then for all non-uniform probabilistic polynomial time algorithms that output and of increasing length k, the probability that and is a negligible function in k.

Then, Boltzmann's entropy formula gives for the probability distribution function, A = const.

Then converges to with probability 1 as.

Then participants were asked to evaluate the probability of her being a feminist, the probability of her being a bank teller, or the probability of being both a bank teller and feminist.

Then he would get to his feet, as though rising in honor of his own remarkable powers, and say almost invariably, `` Gentlemen, this is an amazing story!!

Then, Jesus indicated that God's forgiveness is unlimited.

Certainly, the meaning is clearer to one who is not familiar with Biblical teachings, in the New English Bible which reads: `` Then Jesus arrived at Jordan from Galilee, and he came to John to be baptized by him.

Then it added: `` It is not possible to determine how extensive these ill effects will be -- nor how many people will be affected ''.

Then the words fell into a pattern: `` Mollie the Mutton is scratching her nose, Scratching her nose in the rain.

Then he thought of Aaron Blaustein standing in his rich house saying: `` God is tired of taking the blame.

Then it is marked on the inside where it comes in contact with the transom, frames, keelson and all the battens.

Then it is replaced and fastened.

Then the chines are rounded off and the bottom is rough-sanded in preparation.

Then, a group of eggs is deposited in a cavity in the beebread loaf and the egg compartment is closed.

Then there is a diagonalizable operator D on V and a nilpotent operator N in V such that ( A ) Af, ( b ) Af.

Then in 2 we show that any line involution with the properties that ( A ) It has no complex of invariant lines, and ( B ) Its singular lines form a complex consisting exclusively of the lines which meet a twisted curve, is necessarily of the type discussed in 1.

Then, too, the utmost clinical flexibility is necessary in judiciously combining carefully timed family-oriented home visits, single and group office interviews, and appropriate telephone follow-up calls, if the worker is to be genuinely accessible and if the predicted unhealthy outcome is to be actually averted in accordance with the principles of preventive intervention.

Then the editorial added prophetically: `` how far they may reach in Asia is yet undetermined, but they fall far short of our dreams of the war conferences ''.

Then she catapults into `` everything and everybody '', putting particular violence on `` everybody '', indicating to the linguist that this is a spot to flag -- that is, it is not congruent to the patient's general style of speech up to this point.

Then comes the time when the last wire is removed and Susie walks out a healthier and more attractive girl than when she first went to the orthodontist.

Then, with the new affluence, there is actually a sallying forth into the wide, wide world beyond the precincts of New York.

Then, if the middle number is activated to its greatest potential in terms of this square, through multiplying it by the highest number, 9 ( which is the square of the base number ), the result is 45 ; ;