For n 1, 2, brvbar , let F n and F be d f s such that And let F be continuous Then show that Uniformly in x Atilde Atilde For Icirc micro 0, choose a and b sufficiently small and sufficiently large, respectively, so that F ( a ) Icirc micro 3, F ( yen ) F ( b ) Icirc micro 3 Next, partition a, b by a x 0 x1 brvbar xk 1 xk b, so that F ( xj ) F ( xj 1) Icirc micro 3, j 1, brvbar , k Finally, by taking x Atilde a , b , or x a, or x b, show that F n ( x ) F ( x ) Icirc micro for all x , provided n sup3 N some integer independent of x Atilde Atilde F, S F, n

Question: For n = 1, 2,¦, let F n and F be d.f.s such that And let F be continuous. Then show that Uniformly in x

Forn= 1, 2,€¦, letF_nandFbe d.f.s such that

And let F be continuous. Then show that

Uniformly in x ÃŽ Ã‚.

For Îµ > 0, choose a and b sufficiently small and sufficiently large, respectively, so that F(a) < Îµ/3, F (¥) €“ F(b) < Îµ/3. Next, partition [a, b] by a = x₀ < x1 < €¦ < xk €“ 1 < xk = b, so that F(xj) €“ F(xj €“ 1) < Îµ/3, j = 1, €¦., k. Finally, by taking x ÃŽ [a, b], or x < a, or x > b, show that |F_n(x) €“ F(x)| < Îµ for all x, provided n ³ N some integer independent of x ÃŽ Ã‚?

F, S F, n-

Step by Step Solution

★★★★★

3.35 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

For 0 select a b so that Next F being continuous is uniformly continuous in a b Then ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

742-M-S-P (6919).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let subject to and xj ¥ 0, for j = 1, 2,., n Z* = max aijXj bi, for i = 1,2, . . . , m,

For n = 1, 2,¦, consider the r.v.s X n , X and Y such that | X n | £ Y , ÎµY r 0), and Then show that X. >00

Let f be continuous on a closed, nondegenerate interval [a, b] and set a) Prove that if M > 0 and p > 0, then for every > 0 there is a nondegenerate interval / c [a, b] such that b) Prove that M=...

Math 125 A: Homework 5 Due Thursday, November 9 1. For n = 1, 2, let fn : E R and suppose that fn f uniformly for some function f . Show that if each fn is bounded, then f is bounded. 2. Let {fn } be...

In this question you will be asked to reflect on a project you have been involved in or observed, in which a design evolved, or could have evolved, through applying a theory of user behaviour. You...

Problem 1 : (10 points) Let f : R R be given by the "floor function" f(x) = [x] This means, that f(x) is the largest integer that is less than or equal to x. So, for example, f(3.14) = 3, f(2) = 2,...

The Basics of Financial Mathematics Spring 2003 Richard F. Bass Department of Mathematics University of Connecticut c These notes are 2003 by Richard Bass. They may be used for personal use or class...

Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...

Show the parse trees for the two parses that the grammar assigns for sentence S1. S1: the train station bus rumbles [3 marks] (b) Give an algorithm for a bottom-up passive chart parser without...

Answer all questions. Kindly explain the answers fully. Let {N, : 0 > 0 defined on the probability space (0, F, P) with respect to the filtration F,, 0 X, OSIST i=1 we let > > 0 and consider the...

Sheffield Company prepares monthly cash budgets. Relevant data from operating budgets for 2022 are as follows. Sales Direct materials purchases Direct labor Manufacturing overhead Selling and...

An oil producer discovers an oil supply in Texas that can be pumped for a profit of $50 per barrel now, $60 per barrel in three years, $80 per barrel in five years, or $90 a barrel in seven years....

Cash 120,000 A/c Payable 40,000 A/C Rec 80,000 Capital 100,000 Inventory 40,000 Unearned Commission 20,000 Prepaid Advertising 36,000 Sales 440,000 Cost of Goods Sold 280,000 Salaries Expenses 22,000...

Which of the following is NOT a primary goal of integrated change control? A. Influencing factors that cause change. B. Determining that a change has occurred. C. Managing change as it occurs. D....

There are 100 employees at Kiddie Carts International. Fifty-seven of the employees are hourly workers, 40 are supervisors, 2 are secretaries, and the remaining employee is the president. Suppose an...

Buster Posey of the San Francisco Giants had the highest batting average in the 2012 Major League Baseball season. His average was .336. So assume the probability of getting a hit is .336 for each...

Four womens college basketball teams are participating in a single-elimination holiday basketball tournament. If one team is favored in its semifinal match by odds of 2 to 1 and another squad is...

RAK, Inc., has no debt outstanding and a total market value of $220,000. Earnings before interest and taxes, EBIT, are projected to be $40,000 if economic conditions are normal. If there is strong...

Two projects are listed below. As an analyst within the government, your job is to identify metrics for the projects investment decision criteria. Two such projects have the following criteria:...

Consider the following information concerning three portfolios, the market portfolio, and the risk-free asset: Portfolio R P P P X 12.50 % 34.00 % 1.50 Y 11.50 29.00 1.20 Z 7.10 19.00 .80 Market...