Follow the steps below to prove the LLN without using CLT. (a) Let (X) be a random

Question:

Follow the steps below to prove the LLN without using CLT.

(a) Let $X$ be a random variable with mean $\mu$ and variance $\sigma^{2}$. Then for any real number $\alpha>0, \operatorname{Pr}(|X-\mu| \geq \alpha) \leq \frac{\sigma^{2}}{\alpha^{2}}$.

(b) Apply Chebyshev's inequality to prove the LLN.

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

Step by Step Answer:

Related Book For book-img-for-question

Applied Categorical And Count Data Analysis

ISBN: 9780367568276

2nd Edition

Authors: Wan Tang, Hua He, Xin M. Tu

See More Books

Question Posted: Mar 31, 2024 12:00 AM

See More Questions

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...
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...
Let i and j be positive integers. (i) Prove that there exist natural numbers a and b such that ai = bj+gcd(i, j). You may use standard results provided that you state them clearly. [4 marks] (ii) Let...
Revenue for the new startup company "BCB Excavating" for the years 2017 through 2021 have been $543,000, $603,400, $789,000, $845,000, and $889,000 respectively. Year 2017 2018 2019 2020 2021 2022...
From the following adjustment data, calculate the adjustment amount and record appropriate debits or credits: a. Supplies purchased, $1,000. Supplies on hand, $50. b. Store equipment, $10,000....
Why, under oligopoly, might a particular industry be collusive at one time and yet highly price competitive at another?
A science hobbyist has purchased a surplus transformer that converts $7.2 \mathrm{kV}$ from neighborhood distribution lines into $120 \mathrm{~V}$ for homes. He connects the transformer...
The following data are taken from the records of Saro Corporation and subsidiaries for Year 1: Net income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
Based on the data from six students, the regression equation relating number of hours of preparation (x) and test score (y) is y-hat = 67.3 +1.07x. The same data yield r=0.224 and y-bar = 75.2. What...
Go to the St. Louis Federal Reserve FRED database, and find data on real GDP (GDPC1), potential GDP (GDPPOT), and the unemployment rate (UNRATE) from 1960 to the most recent period. For the...
Suppose $\mathbf{x} \sim M N(n, \boldsymbol{\pi})$ follows a multinomial distribution of size $n$ and probability $\pi$. Derive the variance matrix of $\mathbf{x}$.
The heat loss through the exterior walls of a certain poultry processing plant is estimated to cost the owner $3,000 next year. A salesman from Superfiber Insulation, Inc., has told you, the plant...
(a) What is a construction contract? (b) How and why should construction contracts be combined or segmented? (c) How is the stage of completion determined? (d) What is the effect of variations and...
A companys senior financial officer says, I always follow IFRSs in preparing my companys financial statements. But the IASB Framework is a lot of conceptual theory that doesnt affect me directly. It...
Under the IASB Framework, an asset is recognised when it is probable that the future economic benefits will flow to the entity. (a) Which future economic benefits does that principle refer to?...
An entity reported net income of EUR 250,000 for 2009. The entity had 125,000 ordinary shares of EUR 1 and 30,000 convertible preference shares of EUR 40 each outstanding during the year. The...
A company buys a costly item of electronic equipment that it expects will have a useful life of eight years, and it depreciates the asset over that period. By the end of the fourth year, the item of...
For the water channel flow of Fig P3.178, h1 = 0.45 ft, H = 2.2 ft, and V1 = 16 ft/s. Neglecting losses and assuming uniform flow at sections 1 and 2, find the downstream depth h2. Show that two...
Some people argue that the internal control requirements of the Sarbanes-Oxley Act (SOX) put U.S. companies at a competitive disadvantage to companies outside the United States. Discuss the...
Husband Wife Total Properties acquired before the marriage Properties for exclusive use 70,000.00 20,000.00 90,000.00 Other properties acquired 530,000.00 380,000.00 910,000.00 Properties acquired...
Assume an auditor chooses to test the control that an accounts payable manager signs the invoices to approve payment before payment is made. The auditor notices that there are signatures on the...
What is the act of comparing the amount of a balance sheet account in one year to the amount for the same account in a prior year?

Follow the steps below to prove the LLN without using CLT. (a) Let (X) be a random

Question:

Step by Step Answer:

Applied Categorical And Count Data Analysis

Students also viewed these Statistics questions