Reference no: EM131228858
Question 1. Air America has a policy of routinely overbooking flights. The random variable X represents the number of passengers who cannot be boarded because there are more passengers than seats. The probability mass function of X is as follows:
(i) What is the probability that the number of passengers who cannot be boarded is more than 2 in a randomly selected flight?
|
x 0
|
1 2 3 4
|
5
|
|
P (X = x) 0.55
|
0.25 0.10 0.05 0.03
|
0.02
|
(ii) Write down the cumulative distribution function of X.
(iii) Calculate the mean and standard deviation of X.
(iv) In a random sample of six flights, what is the probability that all the passengers can be boarded in at least half of flights in the sample?
(v) The airline also has another policy of compensation for any passenger affected by overbooking flights. The airline will pay $80 per passenger who cannot be boarded due to overbooking in any flight. Let Y be the total amount of compensations paid to all passengers who cannot be boarded in one particular flight. Write down the probability mass function of Y .
Question 2. Number of motor vehicle death events per month in Dutchess County, New York, is modeled by a Poisson distribution with average of 1.8 per month.
(i) What is the probability that there are more than 3 motor vehicle death events in Dutchess County in a given month?
(ii) What is the probability that in a particular year, there are between 24 to 27 motor vehicle death events, inclusive, in Dutchess County?
(iii) What is the probability that in a given year, there are exactly two months with more than 3 motor vehicle death events per month (it implies that each of the other ten months has less than or equal to 3 motor vehicle death events) ?
Question 3. A zoologist has ten male and seven female guinea pigs. She randomly selects five guinea pigs for an experiment.
(i) What is the probability that more female guinea pigs are selected in the experiment?
(ii) Given that more female guinea pigs are selected in the experiment, what is the probability that exactly four female guinea pigs are selected in the experiment?
Question 4. You are trying to set up a portfolio that consists of Fund X and Fund Y . The following information about the annual return (per $1000) of each of these investments under different economic conditions is available along with the probability that each of these economic conditions will occur in next year.
|
Probability
|
State of Economy Fund X ($) Fund Y ($)
|
|
0.10
|
Recession
|
-160
|
350
|
|
0.15
|
Stagnation
|
-40
|
100
|
|
0.35
|
Slow growth
|
80
|
40
|
|
0.30
|
Moderate growth
|
150
|
-30
|
|
0.10
|
High growth
|
200
|
-100
|
(i) Compute the expected return for the Fund X and for the Fund Y .
(ii) Compute the standard deviation for the Fund X and for the Fund Y .
(iii) Compute the covariance of the Fund X and the Fund Y .
(iv) Suppose that you want to create a portfolio that consists of 25% Fund X and 75% Fund Y . Compute the portfolio expected return and portfolio risk.
(v) Find the probability that your portfolio return is more than $45 per $1000 invest- ment in the next year.
|
Many business offer free samples of their products
: Many business offer free samples of their products or services to potential customers to induce them to become customers. Please write two paragraphs that describe how this strategy can be implemented online. Include how the amount of sampling is lik..
|
|
Description of solid post in announcement area
: This is question 1 of 2 in this Discussion which means you will need to make a substantial post. Make sure you read the description of a solid post in the Announcement Area. (NOTE: Points will be deducted for weak posts). You are required to respo..
|
|
Write a program, based on the sterling structure
: The second should take two arguments of type sterling and return a value of the same type, which is the sum of the arguments. The third should take a sterling structure as its argument and display its value.
|
|
Using the four theories to analyze each dream
: A friend has just described the following dream to you in which they were running from a snake and could never get away from the snake although it never did catch them either. Using the four theories to “analyze” each dream. Your analysis must demons..
|
|
Write down the cumulative distribution function
: STAT 101 INTRODUCTORY STATISTICS Write down the cumulative distribution function of X - calculate the mean and standard deviation of X and in a random sample of six flights, what is the probability that all the passengers can be boarded in at lea..
|
|
Analyze the ethical considerations that apply
: Identify at least 4 laws or regulations that apply to the company. Explain the actions Juanita's company has to take to ensure they are conforming to the requirements of these identified laws and regulations.
|
|
Finding the combination of mixed drinks
: The bartender of your local pub has asked you to assist him in finding the combination of mixed drinks that will maximize his revenue. He has the following bottles available: Since he is new to the business, his knowledge is limited to the following ..
|
|
Unavoidable physical fatigue
: What can you change about the way the work is done to deal with the unavoidable physical fatigue?
|
|
Explian symbols and actions the artist employs in cartoon
: Identify the symbols and actions the artist employs in the cartoon. Explain the cartoon's message, intended audience, and if the artist was persuasive to their intended audience.
|