Category: Probability

1st using your “modern economy” stock, use a reputable website, such as the Yaho

1st using your “modern economy” stock, use a reputable website, such as the Yahoo Finance website. to collect the data of the SP500 for the same time period, and then answer the two questions below.
Q1 use the correlation tool within excell ( or any other software program, such as python ) to compute the correlation between your modern economy stock & the SP 500 over the whole time period of data collected ( i.e use all data collected )
Q2 use the data of the first ten days of this year for the data of your modern economy stock and the SP 500 ( use ticker SPY), and compute the correlation by hand ( i.e. using the formulas from module two’s main lecture notes )
NOTE: you may submit your solutions as an excell file, or paste into another document such as word/pdf where you can add some nice written dialog to explain your solutions. However, if you do use just excell please BOLD your solutions and/or type in some text dialog to explain which solutions are where in the excel file

Favorite Artist is Monica. There is only one song of hers on the playlist of 50

Favorite Artist is Monica. There is only one song of hers on the playlist of 50 songs.
Favorite Genre is RnB. There are 28 songs on the playlist.
I. Determine the probability that the first song to play from the list will NOT be by the favorite artist.
II. If you decide to create a playlist that only includes the songs by your favorite artist from the playlist of 50 songs, determine how many ways the songs in this new playlist can be arranged.
III. State the total # of genres that appear in your list of 50 songs and identify one as your favorite genre.
IV. Based on that genre, create a tree diagram to illustrate the # of ways to choose TWO songs from the list of 50 selected songs.
V. Given that the first song chosen is from your favorite genre, determine the probability that the second song is also from your favorite genre if the playlist is set to shuffle and no song will repeat.
VI. Given that two songs will be chosen, determine the probability that at the least one of the songs will be from your favorite genre.

Class of 2020 has 50 learners , 30 are males and 20 are females whatwhat is the

Class of 2020 has 50 learners , 30 are males and 20 are females whatwhat is the probability of finding a male

1. The manager of an oil refinery must decide on the optimal mix of two possible

1. The manager of an oil refinery must decide on the optimal mix of two possible blending processes of which the input and output per production run are given as follows:
Process Units
Input
Crude A
Crude B
Output
Gasoline X
Gasoline Y
1
5
3
5
8
2
4
5
4
4
The maximum amount available of crude A and B are 200 units and 150 units respectively. Market requirements show that at least 100 units of gasoline X and 80 units of gasoline Y must be produced. The profit per production run from process 1 and process 2 are Rs. 300 and Rs. 400 respectively. Formulate this problem as a linear programming model.
2. A city police department has the following minimal daily requirement for policeman. Note, you are to consider period 1 as following immediately after period 6. Each policeman works eight consecutive hours. Let X denote the number of men starting work in period t everyday. The police department seeks a daily manpower schedule that employs the least number of policemen, provided that each of the above requirements is met. Formulate linear programming model to find an optimal schedule.
Time of Day
Period
Minimal number of police required during a period
2 – 6
1
20
6 – 10
2
50
10 – 14
3
80
14 – 18
4
100
18 – 22
5
40
22 – 2
6
30
3. A car dealer selects his cars for sale very carefully so as to ensure the optimization of his profits. He deals in 4 types of cars A, B, F and G. The purchase value of the cars range at Rs. 60,000, 150,000, 55,000 and 220,000 and the sales value is fixed at Rs. 80,000, 175,000, 75,000 and 250,000 respectively. The probability of sale are 0.8, 0.9, 0.6 and 0.50 respectively during a period of six months. In order to invest Rs. 20,00,000 in his deals, he wishes to maintain the rates of purchase of cars as 3 : 1 : 2 : 4. Work out how and how much he should buy. Formulate this problem as LP model.
4. Use graphical method to solve the following LP problems
Max. Z = 3×1 + 4×2
Subject to
2×1 + x2 ≤ 10
x1 + 3×2 ≤ 12
x1 + x2 ≤ 6
x1, x2 ≥ 0

Continue working on your project. You will now test your hypotheses using boots

Continue working on your project. You will now test your hypotheses using bootstrapping. You should preform two bootstraps one on the categorical and the quantitative. Be sure to include and edits suggested in your instructor’s review or the peer review. Due Monday at Noon.
Please use the data you originally collected for part 1. You will add these new parts to report part 2, 3, and 4.
1. For this project, you must nd some published or existing data. Possible sources include: almanacs, magazines and journal articles, textbooks, web resources, athletic teams, newspapers, professors with experimental data, campus organizations, electronic data repositories, etc. Your dataset must have at least 25 cases, two categorical variables and two quantitative variables. It is also recommended that you are interested in the material included in the dataset.
2. Use bootstrapping to do the analysis.
(a) Compute the standard error for the quantitative variable that you set up the hypothesis test for in part 4 using bootstrapping. Report a 95% confidence interval and decide if you are able to reject or fail to reject your null hypothesis. Create a histogram for your bootstrap distribution.
(b) Compute the standard error for the categorical variable that you set up the hypothesis test for in part 4 using bootstrapping. Report a 95% confidence interval and decide if you are able to reject or fail to reject your null hypothesis. Create a histogram for your bootstrap distribution.2. Use the techniques of the text to repeat your hypothesis test.
3.Use bootstrapping to do the analysis.
(a) Repeat your hypothesis test on the categorical variable utilizing the appropriate formulas for your situation. Compute 95% con dence interval and compare to results from bootstrapping.
4. Add to your report!
(a) Include all items requested above. Include text and graphics describing the processes you have completed.

Your task: submit a single PDF document with the answers to the following proble

Your task: submit a single PDF document with the answers to the following problems.
1. Complete the following (method to implement empirical data in a tree):
a. Determine the 0.05, 0.10, 0.25, 0.50, 0.75, 0.90, 0.95 quantiles for the high temperature recorded on March 17. . The data for years between 1995 and 2014 is shown below.
b. Plot your assessed quantiles as a CDF.
c. Construct a three-point approximation to the distribution using the extended Pearson-Tukey method. Show the three temperatures, fractiles, and probabiltities in a table.
d. Construct an approximation using the extended Swanson-Megill method. Show the three temperatures, fractiles, and probabiltities in a table.
2. Complete the following (method to implement a continuous distribution in a tree):
a. Suppose you know the expected life of an engine is exponentially distributed with a mean life of 1000 hours.
b. Construct a three-point approximation to the distribution using the extended Pearson-Tukey method. Show the three Engine Hours, fractiles, and probabiltities in a table.
c. Construct a three-point approximation to the distribution using the extended Swanson-Megill method. Show the three Engine Hours, fractiles, and probabiltities in a table.
High temperature on St. Patrick’s Day in Chicago
201441
201338
201273
201170
201062
200970
200843
200738
200642
200555
200435
200371
200242
200135
200037
199971
199846
199751
199654
199563

Continue working on your project. You will now analyze one quantitative variable

Continue working on your project. You will now analyze one quantitative variable and generate two graphics. Be sure to include and edits suggested in your instructor’s review or the peer review. Due Monday at Noon.
Please use the data you originally collected for part 1. You will add these new parts to report part 2.
1. For this project, you must find some published or existing data. Possible sources include: almanacs, magazines and journal articles, textbooks, web resources, athletic teams, newspapers, professors with experimental data, campus organizations, electronic data repositories, etc. Your dataset must have at least 25 cases, two categorical variables and two quantitative variables. It is also recommended that you are interested in the material included in the dataset.
2. Utilizing technology, analyze your dataset.
(a) For at least one of the quantitative variables, include summary statistics (mean, standard deviation, ve number summary) and two graphical displays (histogram and box plot). Are there any outliers? Is the distribution symmetric, skewed, or some other shape?
4. For this project you must find some published or existing data. Possible sources include: almanacs,magazines and journal articles, textbooks, web resources, athletic teams, newspapers, professors with experimental data, campus organizations, electronic data repositories, etc. Your dataset must have at least 25 cases, two categorical variables and two quantitative variables. It is also recommended that you are interested in the material included in the dataset.
5. Decide what to analyze.
(a) Set up a hypothesis test for a quantitative variable. You may compare to a suspected parameter or compare two computed statistics. State your null and alternative hypothesis in the correct formatting:
H0: parameter = value
Ha: parameter ≠ value
(b) Set up a hypothesis test for a categorical variable. You may compare to a suspected parameter or compare two computed proportions. State your null and alternative hypothesis in the correct formatting:
H0: p = value
Ha: p ≠ value
6. Add to your report!
(a) Include all items requested above. Include text about each and why these hypothesis decisions were made