Question: (Lamperti20) An urn contains exactly 5000 balls, of which an unknown number X are white and the rest red, where X is a random variable

(Lamperti20) An urn contains exactly 5000 balls, of which an unknown number X are white and the rest red, where X is a random variable with a probability on the integers 0, 1, 2, . . . , 5000.
(a) Suppose we know that E(X) = μ. Show that this is enough to allow us to calculate the probability that a ball drawn at random from the urn will be white.
What is this probability?
(b) We draw a ball from the urn, examine its colour, replace it, and then draw another. Under what conditions, if any, are the results of the two drawings independent; that is, does P (white, white) = P (white)2 ?
(c) Suppose the variance of X is σ2. What is the probability of drawing two white balls in part (b)?

Step by Step Solution

★★★★★

3.48 Rating (171 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The expected value of X is The probability that a white ball is drawn is Thus Thus 5... 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)

M-S-C-R-V (181).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Suppose X is a random variable with an exponential PDF of the form fX(x) = 2e 2xu(x). A new random variable is created according to the transformation Y = 1 X. (a) Find the domain for X and Y. (b)...

Suppose that W is a random variable with E(W4)

The concentration of a reactant is a random variable with probability density function a. What is the probability that the concentration is greater than 0.5? b. Find the mean concentration. c. Find...

Math 3339 _ HOMEWORK 4 Chapter 4: Discrete Distribution For problems 1 - 4 name the type of probability distribution that can be used for each case. Show work IF POSSIBLE for full credit. 1. Of all...

Help....plz. 4:42 P 5 P - 29 ... OB/s U Mil mil @ 21% 9E-12 You have a thoroughly shuffled deck of 52 cards. Each time you choose one card from the deck. The drawn card is put back in the deck and...

Math 3339 EMCF Homework 4 Sections 4.3 - 4.8 Honework will NOT be accepted through email or in person. Homework must be submitted through CourseWare, https://www.casa.uh.edu, before the deadline....

can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...

1. A soft drink company holds a contest in which a prize may be revealed on the inside of the bottle cap. The probability that each bottle cap reveals a prize is 0.2, and winning is independent from...

Applications | RapidIdentity x _ Quizzes 2 * *Course Hero X + X - > C A...

Ellie and Linda are equal owners in Otter Enterprises, a calendar year business. During the current year, Otter Enterprises has $320,000 of gross income and $210,000 of operating expenses. In...

On 1 January 2020, Black company acquired 100% of White company for $ 1000,000. White company net assets book value was $800,000. Equipment (4 years remaining useful life) was undervalued by $80,000...

You notice that PepsiCo ( PEP ) has a stock price of $ 1 0 8 . 2 2 and EPS of $ 6 . 3 2 . Its competitor, the Coca - Cola Company ( KO ) , has EPS of $ 2 . 7 4 . The value of a share of Coca - Cola...

The following are selected accounts from the general ledger of the First Company on December 31, 2016. Show how the corporation's Stockholders' Equity section would appear on the December 31, 2016,...

The Hamilton Company balance sheet on January 1, 2007 was as follows: The Korbel Company is considering purchasing the Hamilton Company (a privately held company) and discovers the following about...

During the year-end audit of the Cressman Corporations financial statements for 2007, you discover the following items: 1. The company had capitalized $57,000 to the Patent account at the beginning...

On March 31, 2016, Carolina Corporation had outstanding 200,000 shares of 8 percent preferred stock with a par value of $10. The stock was originally issued for $13.50 per share. On that date, the...

Castle Lager has just purchased the Jacksonville Brewery. The brewery is two years old and uses absorption costing. It will "sell" its product to Castle Lager at $47 per barrel. Peter Bryant, Castle...

Write your full name in ASCII using eight bits per character with the leftmost bit always 0. Include a space between names and a period after a middle initial.

A small town in Ohio is considering the purchase of a new parking system that would enhance the collection of parking fees while providing additional convenience to shoppers. The hardware requires an...

TSLA4007901 TSLA4103350 TSLA4103351 Total Coupon Rate 1.50% 0.25% 1.25% Last Trade Price $168.30 $85 $81.44 Cost of Debt (Coupon amount / current market price) 0.89% 0.29% 1.54% Outstanding Book...

Which of the following statements is CORRECT? Answer Any forecast of financial requirements involves determining how much money the firm will need, and this need is determined by adding together...