Let X1, . . . , Xn be independent rv’s with mean values μ1, . . . , μn and variances . C...

Let X₁, . . . , X_n be independent rv’s with mean values μ₁, . . . , μ_n and variances . Consider a function h(x₁, . . . , x_n), and use it to define a new rv Y = h(X₁, . . . , X_n). Under rather general conditions on the h function, if the σ_i’s are all small relative to the corresponding μ_i’s, it can be shown that where each partial derivative is evaluated at (x₁, . . . , x_n) = (μ₁, . . . , μ_n). 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).