Use Theorem 4.11 to prove that if (left{X_{n}ight}_{n=1}^{infty}) is a sequence of random variables that converge in
Question:
Use Theorem 4.11 to prove that if \(\left\{X_{n}ight\}_{n=1}^{\infty}\) is a sequence of random variables that converge in probability to a random variable \(X\) as \(n ightarrow \infty\), then \(X_{n} \xrightarrow{d} X\) as \(n ightarrow \infty\).
Transcribed Image Text:
Theorem 4.11 (Slutsky). Let {X} be a sequence of random variables that converge weakly to a random variable X. Let {Y}=1 be a sequence of random variables that converge in probability to a real constant c. Then, 1. Xn+Y X + c as n o. 2. X,Y, dcX as n . 3. Xn/Yn + X/c as n as long as c +0.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (QA)
Answered By
Muhammad Umair
I have done job as Embedded System Engineer for just four months but after it i have decided to open my own lab and to work on projects that i can launch my own product in market. I work on different softwares like Proteus, Mikroc to program Embedded Systems. My basic work is on Embedded Systems. I have skills in Autocad, Proteus, C++, C programming and i love to share these skills to other to enhance my knowledge too.
3.50+
1+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Business questions
-
(i) Write down the linear program relaxation for the vertex cover problem and solve the linear program. [6 marks] (ii) Based on the solution of the linear program in (b)(i), derive an integer...
-
MUST BE CORRECT ANSWERS A small software company has the following simplified cashflow, funded by shareholders' equity of 20,000 and a bank overdraft of 5000: Invoiced money received 2 months after...
-
Use Theorem 4.11 to prove that if \(\left\{X_{n}ight\}_{n=1}^{\infty}\) is a sequence of random variables that converge in distribution to a real constant \(c\) as \(n ightarrow \infty\), then...
-
Explain impact of IT on cross border communication and how to manage cross cultural business communication successfully.
-
A car and a truck are heading directly toward one another on a straight and narrow street, but they avoid a head-on collision by simultaneously applying their brakes at t = 0. The resulting...
-
Plot the dimensionless performance curves for the pump of Prob. P11.35 and compare with Fig. 11.8 of the text. Find the appropriate diameter in inches and the speed, in rev/min, for a geometrically...
-
Refer to the information in Exercise 22-12. Assume that each of the companys divisions has a required rate of return of 7%. Compute residual income for each division. Data From Exercise 22-12 A food...
-
The bank portion of the bank reconciliation for Langer Company at November 30, 2014, was as follows. The adjusted cash balance per bank agreed with the cash balance per books at November 30. The...
-
Kevin made two investments over the past two years. His first investment wasabaseball card thatcost$50.00,whichhe sold three months later for$55.00.The second wasashare of stockinastart-upcompany....
-
In the context of the proof of Theorem 4.3, prove that \[\lim _{n ightarrow \infty}\left|\int_{a}^{b} g_{m}(x) d F(x)-\int_{a}^{b} g(x) d F(x)ight| for any \(\delta_{\varepsilon}>0\). Theorem 4.3...
-
In the context of the proof of the first result of Theorem 4.11, prove that \[P\left(X_{n} \leq x-\varepsilon-cight) \leq G_{n}(x)+P\left(\left|Y_{n}-cight|>\varepsilonight) .\] Theorem 4.11...
-
Susan, a school teacher in Norway, is planning on traveling overseas during her holidays in December. Since most schools are shut in December, the holiday season, Susan wants to determine if there is...
-
The head loss due to friction in turbulent flow in a closed section pipe is given by the Darcy equation: v h = 1 = 1 = 29 All the parameters in the above equation, except for the friction factor, f,...
-
A structural member must be able to support repeated tension-compression loads (load amplitude is 66800 N, R=-1) without experiencing a fatigue fracture for at least 100 000 cycles. The structure...
-
a) b) A force of F= 500 N is applied to the end of the cable that is attached to block A as shown in Figure Q2(a). The masses of block A and block B are 200 kg and 400 kg respectively. The...
-
23) If drive wheel X rotates clockwise at a speed of 10 rpm, how does wheel Y turn? A. O anti c/w, faster B. Oc/w, slower C. O c/w, faster D. O anti c/w, slower E. O anti c/w, same 24) If the drive...
-
Given the Volumetric Analysis of a Natural Gas: CH4 = 67.3% Nitrogen = 9.6% 0 = 2.7% CO = 0.8% CH6 = 15.4% CO = 1.8% H = 2.4% Calculate the A/F ratio by mass considering CO = 10.8% CO2. Note: Use...
-
In this section we discussed examples of ordinary, everyday functions: Population is a function of time, postage cost is a function of weight water temperature is a function of time. Give three other...
-
For the given transfer function: Vo(s) / Vi(s) = (s^2C^2R^2 + 1) / (s^2C^2R^2 + 4sCR + 1) Assumiing that 1/(CR) = 120 PI so write the matlab code to find the magnitude plot
-
In Exploration 2.1, you used an applet to take many samples of words from the Gettysburg Address, found the proportion of short words in each sample, and then created a distribution of the sample...
-
Suppose instead of just asking the respondents whether they have ever faked a phone call, the interviewer said, Research has shown that that 80% of adult Americans with cell phones have faked a phone...
-
A t-distribution is shaped like a normal distribution but is: A. A bit skewed in one direction or the other. B. A bit taller in the middle than a normal distribution. C. Not quite as spread out with...
-
Present value with periodic rates. Sam Hinds, a local dentist, is going to remodel the dental reception area and add two new workstations. He has contacted A-Dec, and the new equipment and cabinetry...
-
The sun is 30 above the horizon. It makes a 60 m -long shadow of a tall tree. Part A How high is the tree? Express your answer in meters. h = Submit Request Answer t 0 ? m
-
As measured in steel at room temperature, the speed of sound is approximately 5000 m/s. What is the wavelength of a sound wave of frequency 1.2 kHz in steel Explain.
Study smarter with the SolutionInn App