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A new form of the expectation integral proposed recently is based on a new discontinuous form of the distribution function. It is shown that this formula can give rise to errors under certain circumstances. An analogous formula can be obtained by partial Stieltjes integration which is more general and does not require modification of definitions of the axiomatic theory of probability.
New results are presented for time averages as statistical averages. Expressions contain cumulative distribution functions rather than probability-density functions. Cases considered are f{x(t)} and g{x(t), y(t)}, where x(t) and y(t) are time sequences. Results are given for mean value, meansquare value and correlation coefficient. Sources of error are discussed.
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