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1. For any set F and point x in a metric space recall that d(x, F ) := inf{d(x, y): y ∈ F }. Let F be a closed set in a normed linear space S with the usual distance d(x, y) := x - y . Show that d(·, F ) isa convex function if and only if F is a convex set.
2. Let U be a convex open set in Rk . For any set A ⊂ Rk let - A := {-x : x ∈ A}. Assume U = -U , so that 0 ∈ U . Let µ be a measure defined on the Borel subsets of U with 0 <>(U ) <>∞ and µ(B) ≡ µ(-B). Let f be a convex function on U . Show that f (0) ≤ ( f dµ/µ(U ). Hint: Use the image measure theorem 4.2.8 with T (x ) ≡ -x.
You have $380,000 in your bank account. The interest rate in your account is 5%. Solve for the following showing your work: How much interest will you accumulate if interest is compounded annually over the next five years?
imagine that exam 1 for statistics 2160 this term will have 62 questions. each question has 5 multiple choice options
musuppose z is the standardization of x zx-musigma where mu and sigma are the mean and standard deviation of x
Suppose the people living in a city have a mean score of 48 and a standard deviation score of 7 on a measure of concerns about the environment.
An electronic test equipment manufacturing company markets a certain piece of specialty equipment. The company has several competitors who currently market similar pieces of equipment.
Fifty-two percent of the students at a certain college are females. Five percent of the students in this college are majoring in computer science. Two percent of the students are women majoring in computer science. If a student is selected at rand..
Calculate 95 percent and 99 percent confidence intervals for u(mean). Using the 99 percent confidence interval, can we be 99 percent confident that u(mean) is at least 42? Explain.
it has been recorded that 10 people get killed by shark attack every year. what is the probability of having 5 or 6
An experiment consists of selecting a card at random from a 52-card deck. Refer to this experiment and find the probability of the event.
determine the error for each of the following forecasts. compute mad and mse. period value forecast error 1 202 - - 2
Find the probability that a) an individual graduate will have a salary over $45000 and b) A group of nine graduates will have a group average over $45000.
a contractor is considering a sale that promises a profit of 20000 with a probability of 0.7 or loss of 7000 with a
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