Question: 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

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 is 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 is approximately linear [e.g., is approximately linear in (1, 2)], then the equation yields approximations 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 function .]

b. If the voltage v across a medium is fixed but current I is random, then resistance will also be a random variable related to I by . If and , calculate approximations to and .

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