STAT 416 SAMPLE FINAL EXAMINATION Fall, 2020 Problem 1 (midterm 1) The joint probability density function (p.d.f.) of the random variables (X, Y ) is f(x, y) = (x2 − y2)e−x 8

1 COMP10200: Sample Test 2 Questions Sam Scott, Mohawk College, Fall 2019 Knowledge and Understanding ___ / 29 These questions test your basic knowledge of

Please type or hand-write your answers and upload to Blackboard. The problems are from the Hennessey and Patterson book, 5th edition.

This class is a hands-on practical, technical, and applied data science course intended to get you experience working on data science projects. In COGS 9 (Introduction to Data Science) you (may have) learned why data and data science are important. This class goes beyond appreciation for what can be done to actually doing it. Often the best way to learn something is to do it yourself. Often, this process will involve attempting to do something, doing it wrong, learning from your mistakes, and then succeeding. That’s part of the data science process. This course is all about the practice of data science.

1. Consider a relation R with attributes ABCDEF GHI with functional dependencies S: S = { AEG → F, B → AD, AG → HI, BG → D } (a) State which of the given FDs violate BCNF. (b) Employ the BCNF decomposition algorithm to obtain a lossless and redundancy-preventing decomposition of relation R into a collection of relations that are in BCNF. Make sure it is clear which relations are in the final decomposition, and don’t forget to project the dependencies onto each relation in that final decomposition. Because there are choice points in the algorithm, there may be more than one correct answer. List the final relations in alphabetical order (order the attributes alphabetically within a relation, and order the relations alphabetically). (c) Does your schema preserve dependencies? Explain how you know that it does or does not. (d) Use the Chase Test to show that your schema is a lossless-join decomposition. (This us guaranteed by the BCNF algorithm, but it’s a good exercise.)

Academic dishonesty includes such things as cheating, inventing false information or citations, plagiarism, and helping someone commit an act of academic dishonesty. Students who violate university standards of academic integrity are subject to disciplinary sanctions, including failure in the course and suspension from the university. Since dishonesty in any form harms the individual, other students and the university, policies on academic integrity are strictly enforced. You should familiarize yourself with the academic integrity guidelines found in the current student handbook at http://www.fullerton.edu/handbook/.

Write your name and SID at the top of every page. Write your answers on the exam sheet in the white space below the questions. When you finish, show your id when you turn in your exam.

Fix positive integers m, n and consider the vector space V of all m ×n matrices with entries in the real numbers R. (a) Find the dimension of V and prove your answer. Please carry out all the steps of your proof. (b) Let P be the subset of V consisting of m×n matrices each of whose row sum is 1. Prove or disprove: P is a subspace of V. (c) Assume m ≥ 2 and n ≥ 2. Find a subspace of V of dimension 2. Please explain your answer, but you don’t have to give a proof.

The goal of this project is to build a visual narrative in the form of a flexdashboard which shows your mastery of data visualization for both exploratory data analysis and to convey information to an audience.

This project is the last deliverable as there is no final exam in this course. You will be able to work in groups of no more than two, and how you divide the work will be obviously up to you. Along with the submission of your project through Blackboard, you will also have to either present for a few minutes during your lab in Week 15, or record a brief 3 minute video demonstrating all aspects of your completed project.