Question: 1ft X1,...,Xn are n independent identically distributed samples of random variable X with PMF (a) How is E[X) related to Px(l)? (b) Use Chebyshev's inequality

1ft X1,...,Xn are n independent identically distributed samples of random variable X with PMF

(a) How is E[X) related to Px(l)?
(b) Use Chebyshev's inequality to find the confidence level a such that M90(X), the estimate based on 90 observations, is within 0.05 of PX(1). In other words, find a such that
P [|M90(X) - Px(l)| ‰¥ 0.05] ‰¤ a.
(c) Use Chebyshev's inequality to find out how many samples n are necessary to have Mn(X) within 0.03 of PX(l) with confidence level 0.1. In other words, find n such that
P [|Mn(X) - Px(1)| ‰¥ 0.03] ‰¤ 0.1.

0.1 0.9 0 otherwise. x=0, Px(x)= x=1,

Step by Step Solution

★★★★★

3.38 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

X has the Bernoulli 09 PMF a EX is in fact the same as P X 1 because X is Bernoulli b We ... 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)

971-M-S-P (9995).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let X 1 ,¦, X n be independent identically distributed (i.i.d.) r.v.s defined on the probability space (W, A , P ) and having d.f. F . Let F n be empirical d.f. defined in terms of the Xi s ;...

Let X1,..., X15 be independent identically distributed N(4.5, 0.88) random variables, with an average . (a) Calculate P(4.2 4.9). (b) Find the value of c for which P(4.5 - c 4.5 + c) = 0.99.

Let X1, . . ., Xn be independent discrete random variables identically distributed as Using CTL, find the approximate value of P X-bar100 > 2), where 0.2, 0,1,2,3,4, 0, otherwise x100 = (1 /100)glx,

Set 4 Due April 26, 2016 BENG 100 S16 1. See iPython notebook on Ted. Fill it in, run it, and make sure it works. Submit on Ted. 2. Suppose that Y is a geometric random variable of parameter p, 1 (a)...

Clint Walker was examining the accounts receivable of Country Music Inc. Its accounts receivable were recorded at $1,500,000. Based on past audits, Walker established tolerable misstatement at 10...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Fn 17. Please answer 1. You buy one share of stock in company C for C10. Each day the price of C either increases by C1 with probability p or decreases by E1 with probability 1-p. These changes from...

Mck questions please help Question 1. Let X and Y be independent random variables that take values in the set (1, 2, 3). Let V = 2X + 2Y, and W = X - Y. (a) Assume that P(X = r) and P(Y = x) are...

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

An irregular example of n1 = 10 districts in New England gave the accompanying savage crime percentages (per million populace). x1: New England Crime Rate 3.5 3.9 4.0 4.1 3.3 4.1 1.8 4.8 2.9 3.1...

(a) Use Mathcad to create an animation showing how contours and three-dimensional plots of the H+2 LCAO MOs 1 and 2 [Eqs. (13.57) and (13.58)] for a plane containing the nuclei change as R changes...

Assume Apex Printing's financial data shows the following data. Based on these data, what is their WACC? Round your answer to the nearest whole percentage with no decimal places. % Equity = $8,000...

Please answer the image on paper and from an expert!

Given this set of unnormalized data, as depicted on the form in Figure 22-53, transform it to 1NF, then 2NF, and then 3NF. Order number Customer number Customer name Customer address Customer...

A recent news report indicated that 20% of all employees steal from their company each year. If a company employs 50 people, what is the probability that: a. Fewer than five employees steal? b. More...

The Orange County Register, as part of its Sunday health supplement, reported that 64% of American men over the age of 18 consider nutrition a top priority in their lives. Suppose we select a sample...

It is estimated that 10% of those taking the quantitative methods portion of the CPA examination fail that section. Sixty students are taking the exam this Saturday. a. How many would you expect to...

Problem 8-20 NPV and Discount Rates [LO 4] An investment has an installed cost of $562,382. The cash flows over the four-year life of the investment are projected to be $191,584, $235,318, $183,674,...

Compare the doses from natural radioactivity with radiation. Natural radioactivity and its detections. Could this situation support predictions made by the linear energy theory?

QUESTION 12 The risk coming from the firm's choice of debt/equity mix is known as: O a. Time value risk O b. Environmental risk. O c. Process risk Od. Financial risk. QUESTION 13 The term structire...