Mathematics

Is Sun Microsystems a good “Strategic” fit for Oracle? Why or why not?

The purpose of the statistics project is to go through the process that a statistician goes through when analyzing new data. You will be asked to do some Exploratory Data Analysis, describe the data using descriptive statistics and plots, answer some questions about probability of future information, create confidence intervals, and describe relations of the data through the use of correlations and linear regressions.For this project you will use StatCrunch (or any other software you are comfortable using.). You will use the data from the StatCrunch Website entitled “Sample College Data.” This is data sampled from universities from a few states on the East Coast and you will use it to work through the sections below. To find the data follow the link to StatCrunch from MyMathLab. In the Data box click the link to “Data sets” and use the search bar to find the data set “Sample College Data”, then open StatCrunch.Section 1 Exploratory Data Analysis: In this section of your analysis you will need to open the data, describe the data by data type, understand the sample size, the number of data points for each row etc.· Think about displaying the categorical (qualitative data) using pie charts or bar charts· For numerical (quantitative) look to show the data using histograms or other appropriate plots.For every plot or piece of information about the data you uncover, please summarize what the plots/information says about the “shape” of the data.Section 2 Descriptive Statistics: In this section you will describe the data using methods we learned for qualitative and quantitative data. This includes frequencies, measures of central tendency, measures of dispersion and any other statistics you may find within the data (percentiles, outlies, etc.).For all descriptive statistics that you find ensure that you summarize each and how/what is describes in the data.Section 3 Probabilities: In this section you will find the probability of several possible outcomes listed below. You will need to use the data to create these probabilities.1. Find the probability that a randomly selected university will be public.2. Find the probability that a randomly selected university will have an Admissions rate equal to 70% but less than 80%.3. Find the probability that a randomly selected university will have an admissions rate below 60% given that it is a private institution.Section 4 Confidence Intervals: In this section you will need to construct 95% Confidence intervals of the mean and variance of all the numerical (quantitative) data. For each please interpret the confidence interval and explain any surprising results.Section 5 Hypothesis Testing: In this section you will make some hypotheses about the data and then use what we learned in lecture/homework to test these hypotheses.1. Is the average Admissions Rate greater than 70?2. Is the average Retention Rate less than 80?3. Is the average Graduation Rate equal to 55?4. Is the average Admissions Rate for Private universities the same as that for Public?Section 6 Correlation and Regression: In this section you will calculate the correlation matrix and discuss any interesting findings or expected findings. You will also build a regression model and compare the coefficients to the correlation matrix.1. Calculate the correlation matrix for the qualitative columns.2. Build a regression model that takes the dependent variable Admissions Rate:a. Do a simple linear regression with SAT Reading as the independent variable.b. Do a simple linear regression with Average Financial Aid as the independent variable.c. Compare the two above outputs to the correlation matrix entries and discuss what you see.3. Build a regression model that takes the Variable Graduation Rate:a. Repeat a-c from part 2 and discuss the results.

Similar problem in LN, § 5.3, Example 5.3.6, 5.3.7. 1. (10 points)Find the critical points (also called equilibrium solutions) of the predator-prey systemx? =?3 x + 2 x y y? = 7 y?8 x yCritical PointsNote: A point is an ordered pair (x,y), and your answer must be a comma separated list of points.Similar problem in LN, § 5.3, Example 5.3.6, 5.3.7. 2. (10 points)Find the critical points (also called equilibrium solutions) of the competing species systemx? = 3 x?x2 ?2 x y y? = 2 y?y2 ?x yEquilibrium Points:Note: A point is an ordered pair (x,y), and your answer must be a comma separated list of points.See in LN, § 5.3, See Examples 5.3.8-5.3.10. 3. (10 points) Part 1: Critical Points Consider the two-dimensional autonomous systemx? =?9 x + x3y? =?2 y(a) The critical points of the system above have the formx0 = [0 0] , x1 =[ x1 0] , x2 =[ x2 0] .where x1 > 0 > x2. Find these components.x1 = x2 =Part 2: The Jacobian Matrix 1Part 3: The Jacobian Matrix at X0 Part 4: The Jacobian Matrix at X1 Part 5: The Jacobian Matrix at X2 See in LN, § 5.3, See Examples 5.3.8-5.3.10. 4. (10 points) Part 1: Critical Points Consider the two-dimensional autonomous systemx? =?16 x + x3y? = 3 y(a) The critical points of the system above have the formx0 = [0 0] , x1 =[ x1 0] , x2 =[ x2 0] .where x1 > 0 > x2. Find these components.x1 = x2 =Part 2: The Jacobian Matrix Part 3: The Jacobian Matrix at X0 Part 4: The Jacobian Matrix at X1 Part 5: The Jacobian Matrix at X2 See in LN, § 5.3, See Examples 5.3.8-5.3.10. 5. (10 points) Part 1: Critical Points Consider the two-dimensional autonomous systex? = 4 y?y3y? =?9 x?y2

Administer the data collection tool you created in the Topic 2 assignment. Using the data you collect, create an Excel table and complete the items below.Create two frequency tables based on two separate questions from your survey.Create a bar graph and a pie chart based on the data in the frequency tables.Determine the class intervals and create frequency distribution for each of the frequency tables.Create one frequency polygon of the data from the frequency distribution.Create an individual Excel document for each of the required items.

The purpose of the statistics project is to go through the process that a statistician goes through when analyzing new data. You will be asked to do some Exploratory Data Analysis, describe the data using descriptive statistics and plots, answer some questions about probability of future information, create confidence intervals, and describe relations of the data through the use of correlations and linear regressions.For this project you will use StatCrunch (or any other software you are comfortable using.). You will use the data from the StatCrunch Website entitled “Sample College Data.” This is data sampled from universities from a few states on the East Coast and you will use it to work through the sections below. To find the data follow the link to StatCrunch from MyMathLab. In the Data box click the link to “Data sets” and use the search bar to find the data set “Sample College Data”, then open StatCrunch.Section 1 Exploratory Data Analysis: In this section of your analysis you will need to open the data, describe the data by data type, understand the sample size, the number of data points for each row etc.· Think about displaying the categorical (qualitative data) using pie charts or bar charts· For numerical (quantitative) look to show the data using histograms or other appropriate plots.For every plot or piece of information about the data you uncover, please summarize what the plots/information says about the “shape” of the data.Section 2 Descriptive Statistics: In this section you will describe the data using methods we learned for qualitative and quantitative data. This includes frequencies, measures of central tendency, measures of dispersion and any other statistics you may find within the data (percentiles, outlies, etc.).For all descriptive statistics that you find ensure that you summarize each and how/what is describes in the data.Section 3 Probabilities: In this section you will find the probability of several possible outcomes listed below. You will need to use the data to create these probabilities.1. Find the probability that a randomly selected university will be public.2. Find the probability that a randomly selected university will have an Admissions rate equal to 70% but less than 80%.3. Find the probability that a randomly selected university will have an admissions rate below 60% given that it is a private institution.Section 4 Confidence Intervals: In this section you will need to construct 95% Confidence intervals of the mean and variance of all the numerical (quantitative) data. For each please interpret the confidence interval and explain any surprising results.Section 5 Hypothesis Testing: In this section you will make some hypotheses about the data and then use what we learned in lecture/homework to test these hypotheses.1. Is the average Admissions Rate greater than 70?2. Is the average Retention Rate less than 80?3. Is the average Graduation Rate equal to 55?4. Is the average Admissions Rate for Private universities the same as that for Public?Section 6 Correlation and Regression: In this section you will calculate the correlation matrix and discuss any interesting findings or expected findings. You will also build a regression model and compare the coefficients to the correlation matrix.1. Calculate the correlation matrix for the qualitative columns.2. Build a regression model that takes the dependent variable Admissions Rate:a. Do a simple linear regression with SAT Reading as the independent variable.b. Do a simple linear regression with Average Financial Aid as the independent variable.c. Compare the two above outputs to the correlation matrix entries and discuss what you see.3. Build a regression model that takes the Variable Graduation Rate:a. Repeat a-c from part 2 and discuss the results.

Please bid if you understand and can finish in 2 hoursHow does the idea of a differential equation tie into finding integrals from Calculus II?2. Please give an example of a differential equation to solve.3. Give a totally unrelated example of an integral to solve.4. Solve each of the problems that you wrote in parts 2 and 3.5. Include a graph of the each original function along with a graph of their solution.6. Include a url that you used or would help others.

Draw on paper the solution x(t) = v1 e?1t + v2 e?2t on the x1x2-plane and then answer the questions below.(a) Based on your graph, select the correct solution curve from the interactive graph below.• Select One • Curve 1 • Curve 2 • Curve 3 • Curve 4 • None(b) Use the graph below to find lim t?+??x(t)?, where ?x(t)? is the length of the solution vector x(t).• Select One • Zero • Infinity • None(c) Introduce the unit vectors u1 = v1/?v1? and u2 = v2/?v2?. Use the graph below to find thelim t?+?u(t), where u(t) = x(t) ?x(t)?, is a unit vector in the direction of the solution vector x(t).[Select One/U1/-U1/U2/-U2/None](d) Use the graph below to find lim t????x(t)?.• Select One • Zero • Infinity • None(e) Use the graph below to find the lim t???u(t), where u(t) = x(t) ?x(t)?[Select One/U1/-U1/U2/-U2/None]9(f) Characterize the zero solution, x0 = 0.• Select One • Source Node • Source Spiral • Sink Node • Sink Spiral • Saddle • Center • NoneComments on the graph below: • The graph is interactive. • You can click on the boxes to turn on and off possible solution curves. • For each possible solution we display: the possible solution curve, the possible solution vectorx(t), and the associated unit vector u(t) = x(t)/?x(t)?. • You can move the time slider to see how each possible solution vector x(t) and unit vector u(t)change in time. • You can move the eigenvectors v1 and v2 by dragging them from the endpoint, and then see howthe curves would change.

Number of Alcoholic Drinks Consumed per Week: 5, 6, 5, 1, 7, 4, 3, 0, 3, 5, 6, 4, 2, 0, 1, 3, 8, 7, 4, 4.1. (2 points). The above distribution captures the number of alcoholic drinks, on average, twenty college age students consume in a week. Using the data, calculate the following and show your work:a. Mean:b. Median:c. Mode:d. Range:e. Variance:f. Standard deviation (note: for this and all future standard deviation calculations, please assume that we are working with a population):2. (2 points). Calculate the Z-scores for the following values randomly selected from the population: 0, 4, 5, 83. (3 points). Using the Z-scores you calculated, identify the below percentages for the area under the curve using “Appendix A – Area Under Normal Curve” and the “Calculating Z-Score Probabilities Handout”.a. What percentage of the distribution would we expect to fall between the Z-score for the value of 0 from the original distribution and a Z-score of 0?b. What percentage of the distribution would we expect to fall between the Z-score for the value of 4 from the original distribution and a Z-score of 0?c. What percentage of the distribution would we expect to fall between the Z-score for the value of 5 and the rest of the distribution to the right of that value?d. What percentage of the distribution would we expect to fall between the Z-score for the value of 0 from the original distribution and the Z-score for the value of 8 from the original distribution?

Miran Anwar, mth 235 ss21 1: Hw19-5.4-SDE-2x2NS-PP-NP. Due: 04/26/2021 at 11:00pm EDT. See in LN, § 5.4, See Subsection 5.4.3. 1. (10 points) Part 1: Critical Points Consider the two-dimensional autonomous systemx? =? 1 2x + xyy? = 3 2y? 1 2xy(a) The critical points of the system above have the formx0 = [0 0] , x1 =[ x1 y1] .Find these components.x1 =y1 =Part 2: The Jacobian Matrix Part 3: The Jacobian Matrix at X0 Part 4: The Jacobian Matrix at X1See in LN, § 5.4, See Subsection 5.4.3. 2. (10 points) Part 1: Critical Points Consider the two-dimensional autonomous systemx? =? 1 4x + 1 2xyy? = y? 1 2xy(a) The critical points of the system above have the formx0 = [0 0] , x1 =[ x1 y1] .Find these components.x1 =y1 =Part 2: The Jacobian Matrix Part 3: The Jacobian Matrix at X01Part 4: The Jacobian Matrix at X1See in LN, § 5.4, See Subsection 5.4.4. 3. (10 points) Part 1: Critical Points Consider the two-dimensional autonomous systemx? =? 1 4x + 1 2xyy? = y? 1 2y2 ? 1 2xy(a) The critical points of the system above have the formx0 = [0 0] , x1 =[ 0 y1] , x2 =[ x2 y2] .Find these components.y1 =x2 =y2 = Part 2: The Jacobian Matrix Part 3: The Jacobian Matrix at X0 Part 4: The Jacobian Matrix at X1 Part 5: The Jacobian Matrix at X2See in LN, § 5.4, See Subsection 5.4.4. 4. (10 points) Part 1: Critical Points Consider the two-dimensional autonomous systex? =?x + xyy? = 9 8y? y2 ? 1 2xy(a) The critical points of the system above have the formx0 = [0 0] , x1 =[ 0 y1] , x2 =[ x2 y2] .Find these components.y1 =x2 =y2 = 2Part 2: The Jacobian Matrix Part 3: The Jacobian Matrix at X0 Part 4: The Jacobian Matrix at X1 Part 5: The Jacobian Matrix at X2See in LN, § 5.4, See Example 5.4.5. 5. (10 points)

Consider the BVP for the function y given byy??+ 25 y = 0, y(0) = 4, y (?5) = 5.(a) Find r1, r2, roots of the characteristic polynomial of the equation above.r1,r2 =(b) Find a set of real-valued fundamental solutions to the differential equation above.y1(x) =y2(x) =(c) Find all solutions y of the boundary value problem.y(x) =Note 1: If there are no solutions, type No Solution. Note 2: If there are infinitely many solutions, use k for the arbitrary constant.See in LN, § 6.1, See Examples 6.1.2-6.1.3. 2. (10 points)Consider the BVP for the function y given byy??+ 36 y = 0, y(0) = 1, y(?) = 1.(a) Find r1, r2, roots of the characteristic polynomial of the equation above.r1,r2 =(b) Find a set of real-valued fundamental solutions to the differential equation above.y1(x) =y2(x) =(c) Find all solutions y of the boundary value problem.y(x) = 1Note 1: If there are no solutions, type No Solution. Note 2: If there are infinitely many solutions, use k for the arbitrary constant.