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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.
of the three levels of strategy that are part of an organizations decision-making hierarchy which level develops annual
Estimate the proportion of severe malaria infection in those with the sickle-cell trait and those without it. In each case, provide the 95% confidence interval (CI) and interpret its value. Based on the estimates and their confidence intervals, w..
If he rolls 25 games with the new ball, averaging 204 pins with a standard deviation of 24.9, can one conclude at a level of significance of .01 that the new ball has improved his game?
cereal is sold by weight not volume. this introduces variability in the volume due to settling. as such the height to
Suppose we wish to estimate the population mean using a confidence interval. When is it appropriate to use a z-score? When is it appropriate to use a t-score?
a brewerys filling machine is adjusted to fill bottles with a mean of 31.2 oz. of ale and a variance of 0.003.
The probability distribution for the possible results of an experiment is given, Determine the mean of the distribution.
motorola used the normal distribution to determine the probability of defects and the number of defects expected in a
To get the best deal for CD player, Jessica called eight appliance stores and asked the cast of a specific model. The prices she quoted are listed below. Show all work. Compute the standard deviation.
Two Psychology majors, in 2 different section of Clinical Psychology, were comparing test scores. The follwing gives the students
This project will only use the Closing Values. Assume that the closing prices of the stock form a normally distributed data set. This means that you need to use Excel to find the mean and standard deviation and then use those numbers and the metho..
let v be the speed in meters per second of an oxygen molecule and let pv be the density function of the speed
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