Let X1, . . . , Xn be independent rv’s with mean values 1, . . . , n and variances 2 1, . . . , 2 n. Consider a function h(x1, . . . , xn), and use it to define a new rv Y
h(X1, . . . , Xn). Under rather general conditions on the h function, if the is are all small relative to the corresponding is, it can be shown that E(Y)
h(1, . . . , n) and V(Y)
 2

2 1 . . .  2

2 n

where each partial derivative is evaluated at (x1, . . . , xn)

(1, . . . , 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 Y
X4 

X 1

1

 X 1

2

 X 1

3



Let 1
10 ohms, 1
1.0 ohm, 2
15 ohms, 2

1.0 ohm, 3
20 ohms, 3
1.5 ohms, 4
120 V, 4
4.0 V. Calculate the approximate expected value and standard deviation of the current (suggested by “Random Samplings,” CHEMTECH, 1984: 696–697).