claudiocamera
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It is possible to express the mean E{x) of a Random Variable in terms of the Reliability Function. In equations:
E{X} = ∫ R(x) dx - ∫ F(x) dx where the limits of the first integral are from 0 to +∞ ; the limits of the second integral are from -∞ to 0; F(x) is the cumulative distribution function of X and R(x) is the reliability function which equals 1 - F(x).
Well, if R(x) = 1- F(x) we can write the first integral with limits 0 to +∞ as :
∫ [1 -F(x)] dx = ∫ dx - ∫ F(x) dx. If it is correct, since we have +∞ as a limit, the first integral on the left side diverges !!! So, what's wrong with my analysis
E{X} = ∫ R(x) dx - ∫ F(x) dx where the limits of the first integral are from 0 to +∞ ; the limits of the second integral are from -∞ to 0; F(x) is the cumulative distribution function of X and R(x) is the reliability function which equals 1 - F(x).
Well, if R(x) = 1- F(x) we can write the first integral with limits 0 to +∞ as :
∫ [1 -F(x)] dx = ∫ dx - ∫ F(x) dx. If it is correct, since we have +∞ as a limit, the first integral on the left side diverges !!! So, what's wrong with my analysis