Then an observation term cannot be applied to something unobservable.

Then both concepts of particle and wave may be attributed to an observation problem of the gear.

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

Then, on considering the lengths of the intervals to decrease to zero, the likelihood function for an observation from the discrete component is

Then Stoke Jones loses his balance and falls, landing in the ice-cold water, and the groups of boys, still inexplicably laughing, head down to pull him out and take him to the infirmary, where he is held for observation.

Then, when a white guy would ask the same question, the professor would say, " That's a very astute observation.

Ruby Cohn, in her book Back to Beckett, writes that " Beckett's favorite line in the play is Hamm's deduction from Clov's observation that Nagg is crying: Then he's living.

Then Rosetta pointed its instruments again towards Comet LINEAR for observation.

Then, with his wife and young son, he visited his native land and other parts of Europe, occupying his time with scientific observation and study.

Then, we generate a random number for each of n trials and use a logical test to classify the virtual measure or observation in one of the categories.

Then a conflict broke out over a pair of eighteen story observation towers.

Then there comes an observation of such merit that all seems set for real progress.

) Then X < sub > i </ sub > is the value ( or realization ) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μ < sub > i </ sub > and variance σ < sub > i </ sub >< sup > 2 </ sup > for all times i. Then the definition of the autocorrelation between times s and t is

Then X is reflexive if and only if each X < sub > j </ sub > is reflexive.

Then X is separable if and only if X ′ is separable.

Then X is compact if and only if X is a complete lattice ( i. e. all subsets have suprema and infima ).

Then all elements of X equivalent to each other are also elements of the same equivalence class.

Then the quotient space X /~ can be naturally identified with a torus: take a square piece of paper, bend and glue together the upper and lower edge to form a cylinder, then bend the resulting cylinder so as to glue together its two open ends, resulting in a torus.

Then the expectation of this random variable X is defined as

Then a presheaf on X is a contravariant functor from O ( X ) to the category of sets, and a sheaf is a presheaf which satisfies the gluing axiom.

Then the joint distribution of X and Y is completely determined by our channel and by our choice of, the marginal distribution of messages we choose to send over the channel.

Then ƒ is invertible if there exists a function g with domain Y and range X, with the property:

* Let the index set I of an inverse system ( X < sub > i </ sub >, f < sub > ij </ sub >) have a greatest element m. Then the natural projection π < sub > m </ sub >: X → X < sub > m </ sub > is an isomorphism.

Then for a specific value x of X, the function L ( θ | x )

Then the emf, E < sub > X </ sub >, of the same cell containing the solution of unknown pH is measured.

Then X has cardinality at most and cardinality at most if it is first countable.

Then A is dense in C ( X, R ) if and only if it separates points.

Then ρ will be the finest completely regular topology on X which is coarser than τ.

Then the Zariski tangent space at a point p ∈ X is the collection of K-derivations D: O < sub > X, p </ sub >→ K, where K is the ground field and O < sub > X, p </ sub > is the stalk of O < sub > X </ sub > at p.

For those who insist upon it the UK Identity and Passport Service will include such purported titles on a British passport as a mere " observation " e. g. ' The Holder is the Lord of the Manor of X ' provided the holder can provide documentary evidence of ownership.

Alfonso X of Castile commissioned the Alfonsine tables, composed of astronomical data based on observation, from which the date of the creation has been calculated to be either 6984 BC.

A prediction interval, consisting of a lower endpoint designated L and an upper endpoint designated U, is an interval such that a future observation X will lie in the interval with high probability, i. e.

An observation deck with panoramic views, restaurants, theaters, shopping malls and the Skywalk X, a thrilling walking tour around the outer rim.

# Under the null hypothesis the distributions of both groups are equal, so that the probability of an observation from one population ( X ) exceeding an observation from the second population ( Y ) equals the probability of an observation from Y exceeding an observation from X, that is, there is a symmetry between populations with respect to probability of random drawing of a larger observation.

# Under the alternative hypothesis the probability of an observation from one population ( X ) exceeding an observation from the second population ( Y ) ( after exclusion of ties ) is not equal to 0. 5.

A puzzling observation recorded as X / 1872 X1, seen by N. R. Pogson in late 1872 from the Madras Observatory, was also speculated to be a recovery of Biela's Comet, though once again this was later shown to have been unlikely.

In that model, the random variables X < sub > 1 </ sub >, ..., X < sub > n </ sub > are not independent, but they are conditionally independent given the value of p. In particular, if a large number of the Xs are observed to be equal to 1, that would imply a high conditional probability, given that observation, that p is near 1, and thus a high conditional probability, given that observation, that the next X to be observed will be equal to 1.

Thus, Y < sub > i </ sup > is the i < sup > th </ sup > observation of the dependent variable, X < sub > ij </ sub > is i < sup > th </ sup > observation of the j < sup > th </ sup > independent variable, j