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Let X1, . . . , Xn be independent rv’s with
where each partial derivative is evaluated at (x1, . . . , xn) = (µ1, . . . , µn). Suppose three resistors with resistances X1, X2, X3 are connected in parallel across a battery with voltage X4. Then by Ohm’s law, the current is
Let µ1 = 10 ohms, σ1 = 1.0 ohm, µ2 = 15 ohms, σ2 = 1.0 ohm, µ3 = 20 ohms, σ3 = 1.5 ohms, µ4 = 120 V, σ4 = 4.0 V. Calculate the approximate expected value and standard deviation of the current (suggested by “Random Samplings,” CHEMTECH, 1984: 696–697).
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Probability and Statistics for Engineering and the Sciences
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