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UCI Engineering Worksheet

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ENGRCEE 11: Homework Assignment 3 Instructor: Dr. Tirtha Banerjee Assigned on: Friday, Feb. 11th, 2022 Due on: Friday, Feb. 25th, 2022; 11:59 pm (PST) Maximum score: 45 points Problem 1 Mortgages for homeowners in California are classified as either fixed rate or variable rate. Suppose that in one metropolitan area, 40% of all mortgage-paying homeowners pay a fixed-rate mortgage. Five homeowners are to be selected at random; let X denote the number among the five who pay a variable rate. (a) Find the probability distribution of X. [Hint: Let F denote a homeowner who pays a fixed-rate mortgage and V denote one who pays a variable rate. Then one possible outcome is FVFFF, with probability (.4) (.6) (.4) (.4)(.4) and associated with a value of X equal to 1. There are 31 other outcomes, each belonging to a certain value of X.] [6 points] (b) Draw the corresponding probability histogram. [3 points] (c) What is the most likely value for X? What is the expected value of X? [3 points] (d) What is the probability that at least three of the five selected pay fixed-rate mortgages? [2 points] [Total: 14 points] Problem 2 A storm runoff X (in cubic metres per second, i.e. cms) from a subdivision can be modeled by a random variable with the following probability density function: f (x) = k 5x − x2 ; for 0 ≤ x ≤ 3 = k (15 − 3x) ; for 3 ≤ x ≤ 5 = 0; otherwise (a) Determine the constant k and sketch the PDF. Write the expression for the CDF, i.e. F (x), and keep it handy for the questions that follow. [6 points] (b) The runoff is carried by a pipe with a capacity of 3 cms. Overflow will occur when the runoff exceeds the pipe capacity. Is the expected value of runoff within the design capacity? [3 points] (c) If overflow occurs after a storm, what is the probability that the runoff in this storm is less than 4 cms? [3 points] (d) The engineer considers replacing this pipe by a larger pipe with a capacity of 4 cms. However, owing to the corruption in the system, there is a 75% probability that the replacement will not be completed prior to the next storm. What is the probability of overflow in the next storm? [4 points] [Total: 16 points] 1 Problem 3 A contractor is going to bid a project, and the number of days, X, required for completion follows the probability mass function: x p(x) 10 0.2 11 0.3 12 0.1 13 0.1 14 0.3 (a) In how many days does the contractor expect the project to be completed? Also, compute V (X). [2.5 points] (b) The contractor’s profit is given by $2000 × (12 − X). What is the p.m.f. for the contractor’s profit? How much profit do they expect to make? [3 points] (c) The contractor learns that their profit can fluctuate up to 34 standard deviations from its expected value. Now, the contractor is willing to bid if there is a chance they can make at least $3500 in profit, but unwilling to bid if their loss can be more than $3000. Based on this, should they bid the project? [3.5 points] [Total: 9 points] Problem 4 The distribution of resistance for resistors of a certain type is known to be normal, with 10% of all resistors having a resistance exceeding 10.256 ohms and 5% having a resistance smaller than 9.671 ohms. What are the mean value and the standard deviation of the resistance distribution? [Total: 6 points] ************************************************************** 2 CEE 81B Homework #8 Civil Engineering Practicum II, Winter 2022 Raster data, Contour, and Maplex Label Engine Due before the start of your next lab session. When submitting your homework, please upload it to Canvas as one single PDF file. The file name should include the assignment number, your first and last name, and your student ID number (e.g., HW8_FirstName_LastName_12345678.pdf). Double (triple) check that all parts of your homework have been saved before submitting. The goal of this homework is to use raster data containing elevations to create elevation contours for Orange County. We will use an ASCII file containing gridded elevation data and the Spatial Analyst tools within ArcToolbox to do this. We will also use the Labeling toolbar to make custom label intervals for the contours. You will need the files within the folder linked on Canvas. The contents should be as follows: • • • • California folder with layer files OrangeCounty folder with layer files PRISM_us_dem_800m_asc folder with raster files Label_Expression.lxp Start your new map document in ArcMap 1. Open a blank map document. 2. Save your new map document. Set up a new File Geodatabase for this homework 3. Right-click your Home folder in the Catalog panel → Select New → File Geodatabase 4. Change the name of your new FileGDB to: HW8.gdb 5. Make it your default GDB for this homework: a. Right-click HW8.gdb → Make Default Geodatabase Add the California and the OrangeCounty layers 6. Change the CA layer’s Symbology to Hollow (because you just want the borders to display, no fill) 7. Change the OC layer’s Symbology to a. Hollow and b. click the “Edit Symbol…” button, c. then the “Outline…”, d. then select the “Boundary, County” style. 1 of 9 a. b. d. c. 2 of 9 Add the Raster file and Clip raster 8. Either drag and drop the PRISM_us_dem_800m_asc.asc file into your map area from the Catalog pane, or use the Add Data button on the toolbar. 9. To clip a raster layer down to the size of OrangeCounty, you will need to use the clip tool for raster layers: a. ArcToolbox → Data Management Tools → Raster → Raster Processing → Clip b. The inputs for this Clip are i. Input Raster: dem_all_US ii. Output Extent: OrangeCounty iii. Output Raster Dataset: confirm it is outputing to your HW8.gdb iv. Click OK i. ii. iii. iv. a. 3 of 9 Use Spatial Analyst Tools to create Contours 10. You will need to enable the Spatial Analyst extension for ArcToolbox. To do this a. Go to the Customize menu b. Select Extensions… c. Turn on the check mark next to Spatial Analyst and Close a. b. c. 11. Go to ArcToolbox → Spatial Analyst Tools → Surface → Contour 12. The inputs for the Contour tool a. Input raster: dem_all_US_Clip b. Output feature class: confirm this will output to your HW8.gdb c. Contour interval: 50 d. Click OK 4 of 9 a. b. c. d. 11. Change the Symbology for the Contour_dem layer 13. Remove the raster layers from the map 14. Change the Contour_dem layer’s Symbology to a. Quantities → Graduated colors b. Value: Contour c. Classes: 12 d. Use the Color Ramp that goes from green, yellow, brown, pink, white e. Click Label → Format Labels i. Reduce the number of decimal places to 2 f. Click OK 5 of 9 Add Labels using Maplex Label Engine 15. Go to the Customize menu 16. Select Toolbars → Labeling 17. Click on the Labeling drop-down in the Labeling menu → Select “Use Maplex Label Engine” 15. 16. 17. 18. In the Labeling toolbar, click the icon of the label with a list to open the Label manager. a. Add a check mark next to the Contour_dem layer in the Label Classes panel b. Change the Text size to 6 c. In the Placement Properties drop-down, select Contour Placement d. Then last, to label only specified contour intervals, we will use the Expression button in the Text String section i. Click the Expression… button ii. Click the Load… button and select the Label_Expression.lxp file iii. Verify and OK 6 of 9 a. i. b. c. iii. ii. 7 of 9 Add your map components and export your map! 19. Go to Layout View 20. Make sure you are zoomed in as so that the Contours and their labels are clearly visible 21. Add: a. Title b. North Arrow c. Scalebar d. Legend with i. 2 columns ii. 0.5 pt Border, with a 10-pt
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