Mean, Median and Mode

2. Find the mean, median, and mode of the following data set: 5 15 9 22 67 42 2 72 81 53 6 70 41 9 42 23

Finite or countable collection of disjoint open intervals and Cantor sets.

a) If {I } is a finite or countable collection of disjoint open intervals with I (a, b), Prove that (m: Measure) b) If U (empty set) is an open set of R, Prove That (U)> 0. c) Let P denote the cantor set in [0, 1]. Prove that m(P) = 0. d) Suppose that U, V are open subsets of R, a,b R with U [a,b] = V [a,b] ...continues

Sequences and Subsets

1) Find a sequence {E } (n =1 to infinity) of measurable sets with E E ………. Such that ( E ) E ) 2) If E is measurable subset of R Prove that given > 0, there exists an open set U E and a closed set F E such that U E) < and E F) < . 3) If E ,E are measurable subsets of [0,1], a ...continues

Sequences : Measurable Subsets and Cantor Sets (2 Problems)

1) a. Let with . If is a measurable subset of R, prove that and are measurable. b. let E =[0,1]Q. Prove that E is measurable and (E)=1. c. let P denote the cantor set in [0,1]. Prove that 2) If E R, prove that ther exists a sequence { } of open sets with E for all n such that = . - ...continues

Measurable functions

1) a. If g is measurable on [a, b] with g(x) 0 for all x [a, b], prove that 1/g is measurable on [a, b]. b. prove that every continuous real- valued function f on [a, b] is measurable. c. if f is differentiable on [a, b], prove that f' is measurable on [a, b]

Prove functions

(See attached file for full problem description) --- 1) a. Let f be defined on [a, b] by f(x) prove directly that f is measurable b. let E be measurable subset of R, and let f be measurable function on E Define the function f and f on E as follows: f (x) = max { f(x), 0}, and f (x) = max{ -f(x), 0}, 1b. prove direc ...continues

Statistics

The average numbers of home runs hit by the Boston Red Sox per game are: 2 divided by 3 = .66 5 divided by 2 = 2.5 6 divided by 1 = 6 7 divided by 0 = 0 Is that correct using the weighted approach?

A thin glass pipe with internal diameter of 3mm was probed into the heart tissue (membrane) and air pressure was applied

A thin glass pipe with internal diameter of 3mm was probed into the heart tissue (membrane) and air pressure was applied... See attached file for full problem description.

Two word problems on Present Value

1. Income from a precious metals mining operation has been decreasing uniformly for 5 years. If income in year 1 was $100,000 and it decreased by $10,000 per year through year 5, the present worth of the income at 10% per year is closest to? A. $310,500 B. $352,200 C. $379,100 2. Income from sales of a certain oil additi ...continues

Volume of excessive space

A thin glass pipe with the internal diameter of 3 mm was probed into a heart tissue (membrane) and air pressure was plied through the pipe to expand the membrane. Assuming its thickness to be negligible, the circular arc of the bulged membrane was to be 3.6mm (see picture below). Find the volume of the excessive space between th ...continues