4. Consider the triangular probability distribution with PDF f(x) = 0 if x <= 0 or x >= 4, x/2 if 0 < x <= 1, (4-x)/6 if 1 < x < 4.

(a) Obtain the CDF F

(b) Obtain its inverse F^-1

(c) Describe the inverse CDF simulation method for this given problem.

A researcher is interested in studying the effect that the amount of fat in the diet and amount of exercise has on the mental acuity of middle-aged women. The researcher used three different treatment levels for the diet and two levels for the exercise. The results of the acuity test for the subjects in the different treatment levels are shown below.

a) Perform a two-way analysis of variance and explain the results. (Show all work)

b) Find the effect size for each factor and the interaction and explain the results. (Show all work)

You need to complete n courses in order to complete your degree. Some of these courses have prerequisites, for example: “course 1 has to be completed before course 3”. Your goal is to find an order to take all n courses and complete your degree.

Observe the following input file. The first line in the file has 2 numbers n and p where n is number of courses and p is the number of prerequisites.

Input:
5 3
1 2
3 1
4 5

The first line indicates that there are 5 courses numbered 1 to 5 and 3 prerequisites “1 should be taken before 2”, “3 should be taken before 1” and “4 should be taken before 5”
The output should an ordered list of the sequence of courses or “Not possible”. You can print any valid sequence. For the above example the output can be 3, 4 1, 2,5 or 4, 3, 1, 5, 2 etc…

Using topological sort (DFS or source removal) create a python algorithm.

Sentinel Company is considering an investment in technology to improve its operations. The investment will require an initial outlay of $245,000 and will yield the following expected cash flows. Management requires investments to have a payback period of 4 years, and it requires a 8% return on investments. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the table provided.)

Required:
1. Determine the payback period for this investment.
2. Determine the break-even time for this investment.
3. Determine the net present value for this investment.

Consider the following scheduling problem. There are n jobs and a single machine. Each job has a length ℓi and a weight wi . The weight wi represents the importance of job i.

a) Let fi be the finishing time of job i. Design a greedy algorithm to minimize the weighted sum of the completion times ∑n i=1 wifi . Your algorithm should run in time O(n log n) and output an ordering of the jobs.

b) Prove the correctness of your algorithm and analyze its running time.

Example: Suppose there are two jobs: t1 = 1, w1 = 2, t2 = 3, and w2 = 1. Doing job 1 first would give f1 = 1, f2 = 4, and a weighted sum of 2 · 1 + 1 · 4 = 6, which is optimal. Doing job 2 first would yield f1 = 4, f2 = 3, and a larger weighted sum of 2 · 4 + 1 · 3 = 11. (Hint: how does the weighted sum change if we swap two adjacent jobs?)

1. Consider placing two point charges on an x-y plane, the first charge, q1, at (x1, y1), and the second charge , q2, at (x2, y2).

2. Derive an expression for the electric potential and field at any arbitrary point (x, y) in terms of q1, q2, x1, x2, y1 and y2.

3. Choose some reasonable values for q1, q2, x1, x2, y1 and y2 and make a rough sketch of what you expect the electric potential/field to look like. Your picture doesn’t necessarily have to be correct, but you should include some justification for why your sketch looks the way it does. 4. Use SageMath to draw the exact electric potential and field using the expression derived above. Below is an example. x, y = var("x y") g = Graphics() g += contour_plot(1.5 + 0.2*x*y, (x, -4, 4), (y, -4, 4), fill=False, cmap="jet", labels=True, contours=[0, 1, 2, 3, 4], label_fontsize=14) g += plot_vector_field((y/2, -x/2) , (x, -4, 4), (y, -4, 4)) g.show() Your final result should look something like the figure below. Note how you can clearly see the two point charges at (1, 2) and (2, 1.5).

problem 08-23 Algo (Using Regression Analysis for Forecasting

Quarter:1,2,3,4

year 1: 2,0,5,5

year 2: 5,2,8,8

year 3: 7,6,10,10

Can you please show me how to step up excel spreadsheet for this problem. How to figure out the problems on this question.

A researcher interviews 50 employees of a large manufacturer and collects data on each worker’s hourly wage (Wage), years of higher education (EDUC), experience (EXPER), and age (AGE). The data is shown below; the data set can also be found on the text website; labeled Hourly Wage. You will be examining the relationships between the following variables: wage and any relationship of this variable to 1) education and 2) experience. Must use either Minitab or Excel to develop both the scatter plots and find the correlation coefficients.

Please use either Minitab or Excel to develop both the scatter plots and find the correlation coefficients.



A. Which variable is the response variable? Which variables are the explanatory variables?

B. Develop a scatter plot comparing wage to education. Interpret the plot.

C. Develop a scatter plot comparing wage to experience. Interpret the plot.

D. Compute the correlation coefficients for wage and education and wage and experience. Then perform a hypothesis test for both correlations to determine if the correlations are statistically significant. Be sure to show the null and alternative hypotheses, decision rule, decisions and conclusions. Use alpha = .05. Note: Since the hypotheses and decision rule are the same for both tests, only need to write those steps once.  

E. Which of the explanatory variables provides the best predictor of the response variable? Support your response by citing both the scatter plot and correlation test.

A researcher interviews 50 employees of a large manufacturer and collects data on each worker’s hourly wage (Wage), years of higher education (EDUC), experience (EXPER), and age (AGE). The data is shown below; the data set can also be found on the text website; labeled Hourly Wage. You will be examining the relationships between the following variables: wage and any relationship of this variable to 1) education and 2) experience. Must use either Minitab or Excel to develop both the scatter plots and find the correlation coefficients.

Please use either Minitab or Excel to develop both the scatter plots and find the correlation coefficients.



A. Which variable is the response variable? Which variables are the explanatory variables?

B. Develop a scatter plot comparing wage to education. Interpret the plot.

C. Develop a scatter plot comparing wage to experience. Interpret the plot.

D. Compute the correlation coefficients for wage and education and wage and experience. Then perform a hypothesis test for both correlations to determine if the correlations are statistically significant. Be sure to show the null and alternative hypotheses, decision rule, decisions and conclusions. Use alpha = .05. Note: Since the hypotheses and decision rule are the same for both tests, only need to write those steps once.  

E. Which of the explanatory variables provides the best predictor of the response variable? Support your response by citing both the scatter plot and correlation test.

One hundred teachers attended a seminar on mathematical problem solving. The attitudes of representative sample of 12 of the teachers were measured before and after the seminar. A positive number for change in attitude indicates that a teacher's attitude toward math became more positive. The twelve change scores are as follows. 4; 8; −1; 1; 0; 4; −3; 2; −1; 5; 4; −2

1.) What is the standard deviation for this sample? (Round your answer to two decimal places.)

2.) What is the median change score? (Round your answer to one decimal place.)

*Please show step by step*