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1. Let f (x ) := |x |p for all real x . For what values of p is it true that (a) f is convex; (b) the derivative f I(x ) exists for all x ; (c) the second derivative f II exists for all x?
2. Let f be a convex function defined on a convex set A ⊂ Rk . For some fixed x and y in Rk let g(t ) := f (x + ty) + f (x - ty) whenever this is defined. Show that g is a nondecreasing function defined on an interval (possibly empty) in R.
Last fall, a sample of n = 36 freshman was selected to participate in a new 4-hour training program designed to improve study skills.
The accounting staff of Poe Inc. has prepared the following pension worksheet. Unfortunately, several entries in the worksheet are not decipherable.
Assume you always reject null hypothesis, regardless of any sample evidence. Determine the probabiliyt of Type II error? P(Type II error).
the aim of this exercise is to show that -1ltpxylt1 for any pair xy of random variables where pxy is the correlation
Find the maximum and minimum prices of the houses a contractor will build to include the middle 65% of the market.
assume that womens heights are normally distributed with a mean of 63.4 in and a standard deviation of 1.7 in.a. if 1
What is the probability the Time/CNN poll will provide a sample proportion within plus-or-minus 0.02 of the population proportion?
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According to a front-page article in The Wall Street Journal, 30% of all students in American universities miss classes due to drinking. If 10 students are randomly chosen, what is the probability that at most 3 of them miss classes due to drinki..
(a) Calculate quarterly seasonal indexes for healthcare claims using the ratio-to- moving-average method. (b) Derive a trendline using the method of least squares. (c) Estimate the seasonally adjusted trend value of healthcare claims for each quarter..
an apprentices decision making philosophy is to always be very optimistic with company funds as promotions for an
Merrill Lynch Securities and Health Care Retirement, Inc., are two large employers in downtown Toledo, Ohio. They are considering jointly offering child care for their employees.
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