Experimental design and optimal decision i general remarks

The problems of an optimal selection of decision function, the design, and the sample size are worked out mainly in separate theories with different objective functions. In applications a unique objective function is given and with respect to this the three components of the statistical approach must be choosen simultaneously. The paper contents initial proposals for such an approach which is demonstrated by the example of parameter estimating in normal distribution. Besides a general theorem of separability and a theorem of duality of two optimization problems of the complete statistical problem are given.