Let (U) be a UNIFORm ([0,1]) random variable and let (left{X_{n}ight}_{n=1}^{infty}) be a sequence of random variables

Question:

Let $U$ be a UNIFORm $[0,1]$ random variable and let $\left\{X_{n}ight\}_{n=1}^{\infty}$ be a sequence of random variables such that

\[X_{n}=\delta\left\{U ;\left(0, \frac{1}{2}-[2(n+1)]^{-1}ight)ight\}+\delta\left\{U ;\left(\frac{1}{2}+[2(n+1)]^{-1}, 1ight)ight\}\]

for all $n \in \mathbb{N}$. Prove that $X_{n} \xrightarrow{\text { a.c. }} 1$ as $n ightarrow \infty$.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Introduction To Statistical Limit Theory

ISBN: 9780367383138

1st Edition

Authors: Alan M. Polansky

See More Books

Question Posted: Mar 15, 2024 02:00 AM

See More Questions

Control Theory allows us to find various useful properties of a system such as stability. Draw a picture of a generic control system, explaining the functions of feedback and the design goals for the...
Two independent threads are run on different processors in a chip-multiprocessor. Each thread simply increments a private counter one million times. The two counters are stored in consecutive memory...
QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...
2) Assume that your widget manufacturing company has a total annual demand of N widgets per year evenly distributed across the year. Each widget cost $b dollars in material and manufacturing costs to...
A tennis player moves back and forth along the baseline while waiting for her opponent to serve, producing the position-versus-time graph shown in FIGURE 2-33. (a) Without performing a calculation,...
A solid, insulating sphere of radius a has a uniform charge density 1 and a total charge Q. Concentric with this sphere is an uncharged, conducting hollow sphere whose inner and outer radii are b and...
Some of the prior interviews suggest that the company is so cheap that they wont pay people what they are worth. Have you had similar experiences?
Victoria Lee Company had the following adjusted trial balance. Instructions (a) Prepare closing entries at June 30, 2017. (b) Prepare a post-closing trialbalance. VICTORIA LEE COMPANY Adjusted Trial...
In return for an investment of $34318 in a fixed interest security, you will receive $134 at the end of each half year plus your money back on redemption in 12 years. You intend to deposit all the...
Let $\left\{X_{n}ight\}_{n=1}^{\infty}$ be a sequence of independent random variables where $X_{n}$ has probability distribution function \[f(x)= \begin{cases}1-n^{-1} & x=0 \\ n^{-1} &...
Let $\left\{X_{n}ight\}_{n=1}^{\infty}$ be a sequence of random variables such that \[\lim _{n ightarrow \infty} E\left(\left|X_{n}-cight|ight)=0\] for some $c \in \mathbb{R}$. Prove that \(X_{n}...
The concentration of a certain drug in a patients bloodstream t hours after being administered orally is assumed to be given by the function C(t) = Ate k t, where C is measured in micrograms of drug...
A ball travels along a straight track with the acceleration a = position of the ball is s = 2ft and the velocity of the ball is v = -2- (3t-4)- When t = ft X 82 ft S ft a. What is the ball's velocity...
An object having emissivity 0.0867 radiates heat at 15 W, when is a temperature is T. if T is doubled what is the rate at which it radiates heat ?
Write the formula of the following coordination compounds: a. Pentaamminecarbonatocobalt(III) Fluoride... b. trans-diamminetetraisothiocyanatochromate(III) ion.
A truck cruising with the velocity 120 km/hour, collides elastically with a cow on the express way. What would be the cow's velocity in the frame of reference of the truck's driver? Why? Two billiard...
In the swing carousel amusement park ride, riders sit in chairs that are attached by a chain to a large rotating drum as shown in (Figure 1). As the carousel turns, the riders move in a large circle...
When a Newtons ring apparatus (Fig. 24-31) is immersed in a liquid, the diameter of the eighth dark ring decreases from 2.92cm to 2.48cm, what is the refractive index of the liquid?
During the month, services performed for customers on account amounted to $7,500 and collections from customers in payment of their accounts totaled $6,000. At the end of the month, the Accounts...
Recall from Exercise 2.4.27 that the increase in joke ratings in the presence of a laugh track. Redo parts (a) through (d) using median as the statistic instead of mean. Data from Exercise 2.4.27...
Recall from Exercise 2.4.29 on the predicted test scores. Redo parts (a) through (d) using median as the statistic instead of mean. Data from Exercises 2.4.29 Right after 27 students in a college...
Do people think they look different than they actually do? In particular, do they think they look better? Researchers Epley and Whitchurch (2008) tried to answer this question by taking pictures of...
Hong won a charity raffle. His prize will be randomly selected from the 9 prizes shown below. The prizes include 4 rings, 3 cameras, and 2 headsets. Prizes 0000 (a) Find the odds against Hong winning...
bring this packet with you to every class as this is an ongoing problem. Chart of Accounts 11. Cash 31. Jolene Upton, Capital 12. Accounts receivable 14. Supplies 15. Prepaid rent 16 Prepaid...
Suppose the wavelength of the photon absorbed when Daniel jumps from levels 2 to 3 is 800 nm. What would be the wavelength of the photon Daniel would have to absorb if he wanted to jump from levels 2...

Let (U) be a UNIFORm ([0,1]) random variable and let (left{X_{n}ight}_{n=1}^{infty}) be a sequence of random variables

Question:

Step by Step Answer:

Introduction To Statistical Limit Theory

Students also viewed these Business questions