Simplify the seatbelt example with a logistic function to approximate the Gaussian distribution of individual strengths. CDF S = pdf S dS 1 + e−a (S−b). Choose your own values for coefficients a and b to reveal a reasonable CDF(S) shape. Obtain a 2-D contour graph of the optimization. Solve it.
Choose your own function of y(x,d), but don’t make it too complicated. Use propagation of variance to determine σy. Compare the x∗ values for a variety of cases, for instance, to minimize σy, to maximize y, to minimize the 95% worst case, etc.
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