Let XX, be independent rv's with mean values ...... , and variances ,..., 2.

Consider a function h(x,, x,), and use it to define a new rv Y=h(X,..., X). Under rather general conditions on the h function, if the 's are all small relative to the corresponding 's, it can be shown that E(Y) h() and V(Y) = + ,x,) = where each partial derivative is evaluated at (x), (H). Suppose three resistors with resistances X, X2, X are connected in parallel across a battery with voltage X. Then by Ohm's law, the current is 1 y = X + + X X3 Let =10 ohms, = = 1.0 ohm, u = 15 ohms, = 1.0 ohm, = 20 ohms, , 1.5 ohms, 120 V, = 4.0 V. Calculate the approximate expected value and standard devia- tion of the current (suggested by "Random Samplings," CHEMTECH, 1984: 696-697).