Consider an rv X with mean and standard deviation , and let g(X) be a specified function of X. The first-order Taylor series approximation to g(X) in the neighborhood of g(x) = g()+g() (X-p) The right-hand side of this equation is a linear function of X. If the distribution of X is concentrated in an interval over which g(-)is approximately linear [e.g., Vx is approxi- mately linear in (1, 2)], then the equation yields approxi- mations to E(g(x)) and V(g(x)).

a. Give expressions for these approximations. [Hint: Use rules of expected value and variance for a linear func- tion ax + b.]

b. If the voltage v across a medium is fixed but current / is random, then resistance will also be a random variable related to I by R = v/l. If , = 20 and = .5, calcu- late approximations to g and R-