Market share. Consumers in a certain area can choose between three package delivery services: APS,GX, and WWP. Each week, APS loses 10% of its customers to GX and 20% to WWP, GX loses 15% of itscustomers to APS and 10% to WWP, and WWP loses 5% of its customers to APS and 5% to GX. Assumingthat these percentages remain valid over a long period of time, what is each company's expected marketshare in the long run?

Answered: X, and WWP. Each week, APS loses 10% of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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2. Pretend it's 2005 and people still use iPods. All iPod owners consider only two options for downloading music to their MP3 players: purchase songs from iTunes, or copy songs from friends' CDs (it's 2005, so people still own CDs, too). With these two options, suppose the weekly inverse market demand for the song “All These Things That I've Done" by The Killers (remember, it's 2005) is p= 1.98 – 0.00198Q Suppose the marginal cost to Apple of you downloading a song is zero. (a) What is Apple's optimal price of "All These Things That I've Done"? (b) How many downloads of “All These Things That I've Done" do they sell? (c) Now suppose Apple sells a version of the iPod equipped with software in which songs played on the iPod must be downloaded from iTunes. For this iPod, the inverse market demand for "All These Things That I've Done" is p downloads for this player? How many downloads do they sell each week? 2.75 – 0.003Q. What is Apple's optimal price of
Although investing all at once works best when stock prices are rising, dollar-cost averaging can be a good way to take advantage of a fluctuating market. Dollar-cost averaging is an investment strategy designed to reduce volatility in which securities are purchased in fixed dollar amounts at regular intervals regardless of what direction the market is moving. This strategy is also called the constant dollar plan. You are considering a hypothetical $1,200 investment in a media company's stock. Your choice is to invest the money all at once or dollar-cost average at the rate of $100 per month for one year. Assume that the company allows you to purchase "fractional" shares of its stock. (a) If you invested all of the money in January and bought the shares for $12 each, how many shares could you buy? shares (b) From the following chart of share prices, calculate the number of shares that would be purchased each month using dollar-cost averaging and the total shares for the year.…
The Harriet Hotel in downtown Boston has 100 rooms that rent for $150 per night. It costs the hotel $30 per room in variable costs (cleaning, bathroom items, etc.) each night a room is occupied. For each reservation accepted, there is a 5% chance that the guest will not arrive. If the hotel overbooks, it costs $200 to compensate guests whose reservations cannot be honored. How many reservations should the hotel accept if it wants to maximize the average daily profit?
What does the fish population of the lake approach in the long run?
A citrus grower anticipates a profit of $100,000 this year if the nightly temperatures remain mild. Unfortunately, the weather forecast indicates a 25% chance that the temperatures will drop below freezing during the next week. Such freezing weather will destroy 40% of the crop and reduce the profit to $60,000. However, the grower can protect the citrus fruit against the possible freezing (using smudge pots, electric fans, and so on) at a cost of $5000. Should the grower spend the $5000 and thereby reducethe profit to $95,000? [Hint: Compute E(X ), where X is theprofit the grower will get if he does nothing to protect the fruit.]
Total DVD and Blu-ray disc sales in 2009 were $8.72 billion. For the purposes of this problem, you will combine DVD and Blue-ray disk sales into one category of DVD sales. A study by In-Stat predicted that "physical disc sales will decline by $4.7 billion by 2014," and that "streaming, on the other hand, should grow from its current $2.2 billion to $6.3 billion over the same time period (2009–2014) a. What is the slope, including units, of the model for DVD sales? Write a statement interpreting the meaning of the slope in the context of the problem. b. Write an equation that represents the linear model for DVD sales. Let D = the sales of DVDs in billions of dollars, and t = the number of years after 2009. c. What is the slope, including units, of the model for streaming videos?
AJ’s sleep pattern had been fluctuating due to stress and diet, so he started to keep a diary of how many hours he slept each night. On the 4th night after he started the diary, AJ slept 9.4 hours, which was the most sleep he got any night. Gradually, he got less sleep each successive night until, on the 18th night after he started the diary, AJ slept 6.2 hours, which was the least sleep he got any night. After keeping his diary for 6 months, he realized that the number of hours he got each night followed a sinusoidal curve. Let t be the number of nights since he started his diary, and s be how many hours he slept that night. It may be helpful to draw a crude sketch of the sleep time function and label the known t − and s − values on it. POSITIVE or NEGATIVE SIN or COS Maximum s − value = Minimum s − value = ______________ ______________ Middle s − value = ______________ = D Amplitude = ______________ = A ⇒ B = ______________ Given the crude sketch of the height function, the…
A computer manufacturer buys 30% of its chips from supplier A and the rest from supplier B. Two percent of the chips from supplier A are defective, as are 4% of the chips from supplier B. Approximately what percentage of the defective chips are from supplier B?
Arbor Systems and Gencore stocks both have a volatility of 44%. Compute the volatility of a portfolio with 50% invested in each stock if the correlation between the stocks is 0.00. If the correlation is 0.00, the volatility of the portfolio is%. (Round to one decimal place.)

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