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

Then the expectation of this random variable X is defined as

Then simple random sampling or systematic sampling is applied within each stratum.

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 ()).

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 ; ;

Then we have informed a large number of our crew that when they reach the United States, they will be punished but that in the meanwhile, they may run loose and are expected to perform their jobs in good order.

Then the king came to the Haye in Touraine and his men had passed the river of Loire, some at the bridge of Orléans and some at Meung, at Saumur, at Blois, and at Tours and whereas they might: they were in number a twenty thousand men of arms beside other ; there were a twenty-six dukes and earls ( Counts ) and more than sixscore banners, and the four sons of the king, who were but young, the duke Charles of Normandy, the lord Louis, that was from thenceforth duke of Anjou, and the lord John duke of Berry, and the lord Philip, who was after duke of Burgoyne ".

Then, in the presence of a large number of foreign journalists, the body of Pasternak was removed to the cemetery.

Then the lists are compared atom by atom ; at the earliest difference, the group containing the atom of higher atomic number receives higher priority.

Then you multiply by the lifetime to get the expected number.

Then the equivalence class of the pair can be identified with the rational number, and this equivalence relation and its equivalence classes can be used to give a formal definition of the set of rational numbers.

Then the number 50 is placed on the stack.

It is frequently stated in the following equivalent form: Suppose that is continuous and that u is a real number satisfying or Then for some c ∈ b, f ( c ) = u.

Then it came under Bern from 1536 to 1798 and a number of its cultural treasures, including the hanging tapestries in the Cathedral, were permanently removed.

Then, as the number of users increases, the system becomes even more valuable and is able to attract a wider user base.

Then the expected number of i type organisms produced by any j type parent is,

Then the total number of i-type organisms after the first round of reproduction, given as, is

Then x is a rational number greater than 0 and less than r < sub > 0 </ sub >.

Then there is a number to show how many athletes are in the boat ( 1, 2, 4 or 8 ).

Then the players roll randomly for a certain number of defects, character age, and characteristics.

Then it was pointed out that " seeing the most submarines " depended not only on the number of submarines present, but also on the number of eyes looking ; i. e., patrol density.

Then a series of explosive asteroids take the planet's shield down, and a number of nasties ( actually, Gith's employees ) invade the planet.

Then the estimated number

In 1986, a screening of the entire Monkees television series by MTV led to renewed interest in the group, followed by a single (" That Was Then, This Is Now " reached number 20 on the Billboard Hot 100 in the U. S .), a 20th Anniversary Tour, a greatest hits album and a brand new LP, Pool It!

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