Let (left{A_{n}ight}_{n=1}^{infty}) be a sequence of events from (mathcal{F}), a (sigma)-field on the sample space (Omega=mathbb{R}), defined
Question:
Let \(\left\{A_{n}ight\}_{n=1}^{\infty}\) be a sequence of events from \(\mathcal{F}\), a \(\sigma\)-field on the sample space \(\Omega=\mathbb{R}\), defined by
\[A_{n}= \begin{cases}{\left[\frac{1}{2}, \frac{1}{2}+n^{-1}ight)} & \text { if } n \text { is even, } \\ \left(\frac{1}{2}-n^{-1}, \frac{1}{2}ight] & \text { if } n \text { is odd }\end{cases}\]
for all \(n \in \mathbb{N}\). Compute
\[\begin{aligned}& \liminf _{n ightarrow \infty} A_{n}, \\& \limsup A_{n},\end{aligned}\]
and determine if the limit of the sequence \(\left\{A_{n}ight\}_{n=1}^{\infty}\) exists.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (QA)
Answered By
Ashington Waweru
I am a lecturer, research writer and also a qualified financial analyst and accountant. I am qualified and articulate in many disciplines including English, Accounting, Finance, Quantitative spreadsheet analysis, Economics, and Statistics. I am an expert with sixteen years of experience in online industry-related work. I have a master's in business administration and a bachelor’s degree in education, accounting, and economics options.
I am a writer and proofreading expert with sixteen years of experience in online writing, proofreading, and text editing. I have vast knowledge and experience in writing techniques and styles such as APA, ASA, MLA, Chicago, Turabian, IEEE, and many others.
I am also an online blogger and research writer with sixteen years of writing and proofreading articles and reports. I have written many scripts and articles for blogs, and I also specialize in search engine
I have sixteen years of experience in Excel data entry, Excel data analysis, R-studio quantitative analysis, SPSS quantitative analysis, research writing, and proofreading articles and reports. I will deliver the highest quality online and offline Excel, R, SPSS, and other spreadsheet solutions within your operational deadlines. I have also compiled many original Excel quantitative and text spreadsheets which solve client’s problems in my research writing career.
I have extensive enterprise resource planning accounting, financial modeling, financial reporting, and company analysis: customer relationship management, enterprise resource planning, financial accounting projects, and corporate finance.
I am articulate in psychology, engineering, nursing, counseling, project management, accounting, finance, quantitative spreadsheet analysis, statistical and economic analysis, among many other industry fields and academic disciplines. I work to solve problems and provide accurate and credible solutions and research reports in all industries in the global economy.
I have taught and conducted masters and Ph.D. thesis research for specialists in Quantitative finance, Financial Accounting, Actuarial science, Macroeconomics, Microeconomics, Risk Management, Managerial Economics, Engineering Economics, Financial economics, Taxation and many other disciplines including water engineering, psychology, e-commerce, mechanical engineering, leadership and many others.
I have developed many courses on online websites like Teachable and Thinkific. I also developed an accounting reporting automation software project for Utafiti sacco located at ILRI Uthiru Kenya when I was working there in year 2001.
I am a mature, self-motivated worker who delivers high-quality, on-time reports which solve client’s problems accurately.
I have written many academic and professional industry research papers and tutored many clients from college to university undergraduate, master's and Ph.D. students, and corporate professionals. I anticipate your hiring me.
I know I will deliver the highest quality work you will find anywhere to award me your project work. Please note that I am looking for a long-term work relationship with you. I look forward to you delivering the best service to you.
3.00+
2+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Business questions
-
5) On the graphs below show the difference between a change in price and a change in demand. Fully label graphs for full marks! (2+2 marks) Change in price Change in demand X 6) A change in the price...
-
"internet radios" for streaming audio, and personal video recorders and players. Describe design and evaluation processes that could be used by a start-up company to improve the usability of such...
-
Let \(\left\{A_{n}ight\}_{n=1}^{\infty}\) be a sequence of events from \(\mathcal{F}\), a \(\sigma\)-field on the sample space \(\Omega=(0,1)\), defined by \[A_{n}= \begin{cases}B & \text { if } n...
-
On February 1, 2020, Sheridan Company sells merchandise on account to Carla Vista Company for $6490. The entry to record this transaction by Sheridan Company is Sales Revenue Accounts Payable Notes...
-
The period T of a simple pendulum is the amount of time required for it to undergo one complete oscillation. If the length of the pendulum is L and the acceleration of gravity is g, then T is given...
-
A Geiger tube is a radiation detector that essentially consists of a closed, hollow metal cylinder (the cathode) of inner radius ra and a coaxial cylindrical wire (the anode) of radius rb (Fig....
-
In 2014, Air Asia Flight No. 8501 crashed in the Java Sea while flying from Indonesia to Singapore. The crash resulted in the deaths of all passengers and crew on board. The plane involved in the...
-
Speedy Oil provides a single-channel automobile oil change and lubrication service. Customers provide an arrival rate of 2.5 cars per hour. The service rate is 5 cars per hour. Assume that arrivals...
-
Cash Receipt Schemes and Other Asset Misappropriations, identify and describe two big data and data analytic techniques each for detecting skimming, cash larceny, and noncash misappropriations.
-
Consider a probability space \((\Omega, \mathcal{F}, P)\) where \(\Omega=(0,1), \mathcal{F}=\mathcal{B}\{(0,1)\}\) and \(P\) is Lebesgue measure on \((0,1)\). Let...
-
Let \(\left\{A_{n}ight\}_{n=1}^{\infty}\) be a sequence of events from \(\mathcal{F}\), a \(\sigma\)-field on the sample space \(\Omega=\mathbb{R}\), defined by \(A_{n}=\left(-1-n^{-1},...
-
Why do MNE managers need to develop an understanding of changing economic conditions in nontriad regions?
-
4. A lens has a strong spherical aberration. If an object consists of a series of dots arranged in a cross concentric with the optical axis (Fig. 1), how does the image look like in the imaging...
-
(A) Consider a particle in one dimension in the presence of a potential V = a|x|; a > 0. The potential is infinite for x 0. Using WKB approximation find its energy. [note: the potential is with no...
-
3. A battery-powered toy travelling at 2.2 m/s drives off a diving board which is at a height above the water. If the impact speed of the toy is 7.3m/s, find the height of the diving board above the...
-
The lowest resonant frequency, in a certain string clamped at both ends, is 50 Hz. When the string is clamped at its midpoint, what is the lowest resonant frequency? (Ans: 100 Hz)
-
Let's say an object moves along the x - axis with the following velocity given as, vx(t) = (a +43 t - 3y ++ 76 t5), where a, , y, and 8 are just constants. (A) Determine an expression for the...
-
Light of wavelength 680nm falls on two slits and produces an interference pattern in which the fourth-order fringe is 38mm from the central fringe on a screen 2.0m away. What is the separation of the...
-
Suppose that you could invest in the following projects but have only $30,000 to invest. How would you make your decision and which projects would you invest in? Project Cost $ 8,000 11,000 9,000...
-
When you hand in your test, do you think you will get a higher score than you actually do? A professor collected data to answer this question in a college mathematics course. After finishing a test,...
-
Do people think bottled water tastes better than tap water? In a blind taste test, student researchers asked 31 subjects to rate the taste of two waters, one bottled and one tap, on a scale from 1 to...
-
Is a basketball players ability to make free throws different when they get their own rebound or when someone else gets their rebound for them? This is what student researchers wanted to explore. The...
-
Suppose a satellite is in a low-Earth orbit. Is it possible that the satellite will eventually fall to the ground? Why or why not
-
The velocity components of and of a two-dimensional flow are given by = 22 and = 22 where and are constants. Calculate the acceleration
-
If this had been on Mars the slope would have been 3.7N/kg. What can you determine about the strength of Mars' gravitational field
Study smarter with the SolutionInn App