By Lehn Wegmann

Eine elementare Darstellung statistischer Schätz - und Testverfahren einschließlich der zugrundeliegenden Modellbildung für Mathematiker, Informatiker, Wirtschaftswissenschaftler, Naturwissenschaftler und Ingenieure.

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**Additional resources for Einfuehrung in die Statistik**

**Example text**

In this book it will not be possible to discuss many-dimensional random variables in detail. We will indicate only some expressions involving two-dimensional continuous random variables (the corresponding formulae for two-dimen sional discrete random variables will have an analogous form). 35) >al part of the probability that (ξ, η) takes a which is the principal \x < ξ < x + dxl value in the rectangle , (see Fig. & 14). The funcly < η < y + dy\y ' tion φ(χ9 y) is called a two-dimensional probability density function.

This enables us to obtain probabilities graphically from the cumulative distribution curve (Fig. 10), if the scale is properly chosen so that F( + oo) = 1. The cumulative distribution function is suitable for discussing problems involving both discrete and continuous random vari ables (and also random variables of a more complicated nature). However, its application generally requires special mathematical apparatus (the Stieltjes integral) which lies outside the scope of this book. § 9 . FUNCTIONS OF RANDOM VARIABLES Let f{x) be a single valued function defined on the range of the random variable ξ.

E linear function. For the linear functionrç= a -f- 61 we have: y=f(x) = a+bx; x=g(y) = (y-a)lb; g\y) = l/b . t FIG. 32) We leave the following to the reader: if the random variable ς is uniformly distributed on the interval (