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In this paper we consider the probability density function (pdf) of a non-central χ 2 distribution with arbitrary number of degrees of freedom. For this function we prove that can be represented as a finite sum and we deduce a partial derivative formula. Moreover, we show that the pdf is log-concave when the degrees of freedom is greater or equal than 2. At the end of this paper we present some Turán-type inequalities for this function and an elegant application of the monotone form of l'Hospital's rule in probability theory is given.

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In this paper we present a modelling activity, which was a part of the project DQME II 3 and some general observations regarding the maladjustments and rational errors arising in such type of activities.