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1. Suppose that a real-valued function f on an open interval J in R has a second derivative f II on J . Show that f is convex if and only if f II ≥ 0 everywhere on J .
2. Let f (x, y) := x 2 y2 for all x and y. Show that although f is convex in x for each y, and in y for each x , it is not convex on R2.
3. If f and g are two convex functions on the same domain, show that f + g and max( f, g) are convex. Give an example to show that min( f, g) need not be.
The chance both flights are full is 0.6. Are the two flights being full independent events and What was the mean ranking for the females in this class
a manufacturer wants to increase the absorption capacity of a sponge. based on past data the average sponge could
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Flu cases this past fly season in the Central City school system were about 15 per week. For the entire state, the weekly average is 16 and the standard deviation, 2.35. Are the kids in Central City as sick as the kids throughout the state?
With a mortgage of $48,000 for 15 years with a rate of 11%, what are the total finance charges
Listed below are measured loads (in lb) on the left femur of crash test dummies used in the same cars listed in the Chapter Problem. Use a 0.05 significance level to test the null hypothesis that the different car categories have the same mean. Do..
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Normal distribution with a standard deviation of 800. what sample size would be required to be 95% certain of estimating the mean error to within 150 of the true value?
a piston cylinder compressor is available for evaluation. the device has an initial volume at the beginning of
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