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In this paper the author gives the state probabilities of the following queue model. The arrival and departure precess are at random with λ-mean arrival and μ=mean servicing time in a single channel. The number of channels is in this model a random number depending upon the length of the queue; when the number of waiting units is M and it arrives another unit, the number of channels is increased in one, and this channel services the first unit in queue; when a channel is free and none unit being in queue, this channel es cancelled. Only in the case of the last channel this should be open. So we have the length of the queue is never greater than M. The notation used in the paper is: r=number of units in queue. s=number of channels (of number of elements being serviced). $$\rho = \frac{\lambda }{\mu }$$ P( r,s;t)=Probability of the state ( r, s) on time t. p(r s)=Probability of the state ( r, s) in the steady state of the model. With this notation, we have This model includes as particular cases the model of a single channel, equivale to M-→∞ and the model of infinite channels, equivalent to M=0. [ABSTRACT FROM AUTHOR]

The author define the Median-Regression curve of a bidimensional distribution f(x, y) as the locus y=g(x) of the median of conditional distribution f(y/x). The general propieties of this Median Regresión are given in numbers 1.1 to 1.6 spanish text. As g(x) is not easy to obtain the author introduce, like minimum mean square regression, the minimuni mean regression, as a regression curve that minimize the mean deviation instead of mean square deviation; first the linear mean regression, and further the polinimial mean regression, that ones have some propietioes of regression curve y=g(x). In the empirical distributions the calculus of mean regression involve to find the minimum of a linear expression, with the variables constrained to some inequalities, as in the linear programming, the author discuss some espacial points of this linear programing problem in the third part of the paper. [ABSTRACT FROM AUTHOR]

In order to apply the Hitchcock transportation problem to practical cases, it is very helpful to have a method as simple and brief as possible. The author considers a special case of application of this problem to railways, that of the distribution of empty cars. He recalls how this problem is solved by Dantzig's simplex method and he shows the specially simple values of the coefficients appearing in this case in the simplex tableaus. The great simplification which results makes possible the application of an abbreviated method contained in works of Dantzig and Ricossa. In this paper, (following the conventional terminology and notation for this question) there is given a demonstration of the method based on the arrangement in a tableau of the values of the non-zero solutions λ of the requirement equations system of the problem. So that a group of m+n−1 λ′ will correspond to a basic group vectors P of coefficients of the system, it is necessary for the λ′ to occupy such positions that a chess castle's closed run can not be performed over them. The necessary theory is given to demonstrate this result and consequences are drawn for the selection of an initial basis in the basis changing processus. There is shown how to follow the subsequent calculus by this method, very easily and quickly, until the arrival at the optimal solution or solutions. Finally, the manner of dealing with degeneracy is indicated. [ABSTRACT FROM AUTHOR]

A general survey of non central distribution is given, beginning with well known definitions and expressions of the non central Student's distribution of which different alternatives are presented, for example in terms of the moments of a truncated normal distribution, and followed by the generalised n. c. t distribution. The explicit formulae of its moments and coefficients of skewness and kurtosis are derived, as well as approximations of the same for large values of n (number of degrees of freedom). The above obtained expressions being comparatively difficult to handle, a transformation to normalise the non central t distribution is found, and the general form of the corresponding approximate moments and coefficients, summarised in two main alternatives, one for γ=0, and the other for γ=0. Some special cases are then discussed with detail, and examples of possible applications are widely exposed. Other non central distributions are briefly considered, based on the distribution of semirange, studentised range and analogues of n.c.t, and finally the generalised T distribution, which opened the way for new lines of research and which will be the subject of a subsequent paper. [ABSTRACT FROM AUTHOR]

In this paper a way to determinate the value of a finite game is shown making a secuence of matrices with the values of the games determinate by submatrices of the matrix of the game and looking for saddle point in this matrices. [ABSTRACT FROM AUTHOR]

This paper deals with contingency tables n by n in conexion with the case of quantitative observations of random variable arranged in n groups according to n different caracteristics. The subjet is to give a general method to test either the independence of the n caracteristics, either the independence of any sugroup of them. The method is a generalization of the two caracteristics case as stated in Cramer's «Mathematical Methods of Sstatistics». [ABSTRACT FROM AUTHOR]

It is presented in this paper a definition of the equivalence of two rectangular games. It is not compared every value M( x, y) of the payoff function of one of the games with any value M′( x′, y′) of the payoff function of the other game, and when two values are compared they are not necessarily equal. Also the ε-equivalence for two games indicating some properties is defined. [ABSTRACT FROM AUTHOR]

This paper is concerned with tests of distribution free methods in sequential form. One of the most outstanding features of this methods is the broad field of application, we don't need almost any assumption about the distribution function of the random variable that we study. Unfortunately this distribution free methods need a large sample size to get the neccessary accuracy, so the usefulness of sequential methods that have great savings in average sample size. The distribution free test in sequential form has two very important proprieties, broad field of application and a small average sample size. In the first chapter the author give a test S for the median of any distribution, that, in the case of normal distribution has one relative efficiency of 60% againts Wald sequential test, and about 120% against current most powerful test. So we can use this test S instead of the most powerful test with advantage in sample size and in numerical calculus, because the test S is very simple. In the second chapter, the previous tests S is adapted to 'two sample problem', in first time with alternative hypothesis of differences in location, and then generalized to any alternative. With normal distribution and alternative hypothesis of differences in location the test presented by the author is most powerful and smaller in sample size than other usual tests, Wilcoxon, Wald and Wolfowitz, Epstein, Tsao. In the chapter three the author study the tests of randomness in a similar way. [ABSTRACT FROM AUTHOR]

In the planning of a building we find the following situation We have several dependences with the entrance in the same corridor, and this corridor has one door only to street; we know also the proportion of people wich go out from dependence i to extreme A or extreme B (see figure in Spanish version). The question is: In what place we must put the door P to became minimun the total walking for the people going out. The author in this paper give the answer of this question and in the most general case with densities functions instead of proportions. [ABSTRACT FROM AUTHOR]

This paper concern with some questions of independence of random variables. In § 2 we give some definitions and a generalization of Bernstein's example, that show that n random variables may be independents by subsets, but the total set are not independt (§ 3), and also this fact holds in continue variables. In § 6 we give a measure of independence in two and n dimensions (§ § 1, 8) and on use that measure with the Normal distribution (§ § 9, 10, 11) and others distributions (§ § 12, 13). [ABSTRACT FROM AUTHOR]

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