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About the Production of the Continuous X-Ray Spectrum by Sommerfeld A.

By Sommerfeld A.

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1. Replicate the text example experiment test program (at least) five times by running microcomputer program RANDOM2 with nelpri ¼ 4, ndigit ¼ 2, each time using a different set of three, three-digit odd seed numbers. Write the associated conceptual and estimated statistical models. Then, numerically explain the respective [est(csdm)]’s and their associated [est(CRSIEEi’s)]’s as the sum of their actual values plus realizations of the corresponding intrinsic statistical estimation error components.

Rather each est(CRSIEEi) is equal to the actual value for its corresponding CRSIEEi plus the realization of its intrinsic statistical estimation error component, which, in this numerical example, is equal to À4:25. This elementary example is intended to support two fundamental statistical concepts. First, every statistical estimate, whatever its associated statistical estimator (estimation expression), is the sum of the actual value for the quantity being estimated plus an intrinsic statistical estimation error component.

In our hybrid column vector notation, its magnitude is established by its scalar coefficient. Statistical Estimator . . . . The estimation expression (algorithm) that is used to compute the statistical estimate of the actual value for a conceptual parameter (or its scalar coefficient). Leastsquares and maximum likelihood statistical estimators are employed in this text. Statistical Estimate . . . . The realization value obtained by appropriately substituting the experiment test program datum values into the corresponding statistical estimator (estimation expression, estimation algorithm).

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