Then the required information is collected from a simple random sample of the elements within each selected group.

However, this simple model ends with the bandwidth of the network: Then congestion comes on the network and not with the peers.

The algorithm for deciding this is conceptually simple: it constructs ( the description of ) a new program t taking an argument n which ( 1 ) first executes program a on input i ( both a and i being hard-coded into the definition of t ), and ( 2 ) then returns the square of n. If a ( i ) runs forever, then t will never get to step ( 2 ), regardless of n. Then clearly, t is a function for computing squares if and only if step ( 1 ) terminates.

Then the nerve layers identify simple shapes, such as bright points surrounded by dark points, edges, and movement.

Then he defined it for more complicated functions as the least upper bound of all the integrals of simple functions smaller than the function in question.

Then, using a simple greedy algorithm, the easy knapsack can be solved using O ( n ) arithmetic operations, which decrypts the message.

Then, the presiding officer makes a formal, but simple statement to the House, acquainting each House that the Royal Assent has been granted to the acts mentioned.

Then, combined with the wage Phillips curve 1 and the assumption made above about the trend behavior of money wages 2, this price-inflation equation gives us a simple expectations-augmented price Phillips curve:

Then P diagonalizes A, as a simple computation confirms:

Then it was compressed using a simple run-length encoding scheme and sent down to the ground at 200 bit / s.

Then the integral in Mercer's theorem reduces to a simple summation

Then, in 1978, the company joined the generics movement with the introduction of 16 " No Name " items, marketed in simple black and yellow packaging but otherwise devoid of any branding.

Then the first railroad connecting Puerto Cortes with San Pedro Sula was developed in the 1880s, reducing Omoa to a simple backwater fishing village.

Then they were asked immediately to perform a simple task and a difficult task and their performance in both tasks were assessed.

Then the intersection number of two closed curves on X has a simple definition in terms of an integral.

Then g has a transcendental branch point if z < sub > 0 </ sub > is an essential singularity of g such that analytic continuation of a function element once around some simple closed curve surrounding the point z < sub > 0 </ sub > produces a different function element.

Suppose that R is an algebra over the field C of complex numbers and M = N is a finite-dimensional simple module over R. Then Schur's lemma says that the endomorphism ring of the module M is a division ring ; this division ring contains C in its center, is finite-dimensional over C and is therefore equal to C. Thus the endomorphism ring of the module M is " as small as possible ".

Then is totally unimodular if and only if every simple arbitrarily-oriented cycle in consists of alternating forwards and backwards arcs.

Then, all the animating forces of the state are vigorous and simple, and its principles are clear and luminous ; it has no incompatible or conflicting interests ; the common good makes itself so manifestly evident that only common sense is needed to discern it.

Then, the Schrödinger equation takes the simple form:

Suppose that c is a simple closed curve in a closed, orientable surface S. Let A be a tubular neighborhood of c. Then A is an annulus and so is homeomorphic to the Cartesian product of

Then, the population ate a simple fish stew known in Greek as ' kakavia.

Then, it moves on to a simple chromatic theme, and then back to the opening theme.

Then followed a period of decline: the spa lost its drive and popularity, and degraded to a simple political meeting point, by 1800 already.

Then the expectation of this random variable X is defined as

Then the random number of successes we have seen, X, will have the negative binomial ( or Pascal ) distribution:

Then the statistician must analyze the properties of and, which are viewed as random vectors since a randomly different selection of n cases to observe would have resulted in different values for them.

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

Then Professor Marvin Zelen, a statistician and associate of the recently founded Committee for the Scientific Investigation of Claims of the Paranormal ( CSICOP, now known as the Committee for Skeptical Inquiry ( CSI )), proposed in a 1976 article in the same periodical that, in order to eliminate any demographic anomaly, Gauquelin randomly pick 100 athletes from his data-set of 2, 088 and check the birth / planet correlations of a sample of babies born at the same times and places in order to establish a control group, giving the base-rate ( chance ) expectation for comparison ( The 100 random athletes later expanded into a subsample of 303 athletes ).

Then under such a rotation, a random phase,, will be created between the eigenstates, of.

Then, each student ’ s score would be a realization of one of a set of independent and identically distributed random variables, with a mean of 50.

Then, a tail event is an event whose occurrence or failure is determined by the values of these random variables but which is probabilistically independent of each finite subset of these random variables.

Then, a particle is placed in a random position of the screen, and moved randomly until it bumps against the seed.

Then we apply the law of total expectation to each term by conditioning on the random variable X:

Then random " noise " words can not be used as successfully to fool the filter.

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

Then a random selection is made similar to how the roulette wheel is rotated.

Then to commit to a bit b Alice picks a random input x and sends the triple

Then, Victor enters the cave and shouts the name of the path he wants her to use to return, either A or B, chosen at random.

Then, we add the segments from the subdivision, one by one, in random order, refining the trapezoidal decomposition.

Then, three of the elements would be selected at random, and then the therapist would ask :" In relation to … ( whatever is of interest ), in which way two of these people are alike but different from the third "?

Then a coupling of and is a new probability space over which there are two random variables and such that has the same distribution as while has the same distribution as.

are identically distributed random variables that are mutually independent and also independent of N. Then the probability distribution of the sum of i. i. d.

Then let the random variables X < sub > i </ sub > indicate the number of times outcome number i was observed over the n trials.

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.

Now let G be some graph, let v be a vertex of G, and let R be a random walk on G starting from v. Let T be some stopping time for R. Then the loop-erased random walk until time T is LE ( R ()).