Question:

Defining a direction for your database and describing how it will be used is a great first step, and this what you accomplished for Iteration 1, but this is just the beginning of the process. Your goal is a live database that supports the organization or application that uses it; several more components need to be created to make this happen. You will create two such components in this iteration.

Your next step is to design your database at a higher level more formally. Structural database rules are a great place to start, a useful tool to frame and guide your design. Structural database rules are written carefully to ensure that they define specific components and constraints for your database. You create these for your database in this iteration, then create entity?relationship diagram (ERD), a universally accepted method of visualizing database schemas. With your structural database rules and ERD, you can articulate and visualize the data and relationships that exist in your mind for your database. Structural database rules and ERDs are the foundation of your database design.

Project Direction Overview

Update the overview that describes who the database will be for, what kind of data it will contain, how you envision it will be used, and most importantly, why you are interested in it.

Use Cases and Fields

Update the five or more use cases that enumerate steps of how the database will be typically used and identify significant database fields needed to support each use case.

Structural Database Rules

Replace this with a list of structural database rules for all significant entities and relationships, with the constraints defined, based upon the use cases you defined, along with supporting explanations.

Conceptual Entity-Relationship Diagram

Replace this with an initial conceptual ERD that visualizes the structural database rules, along with supporting explanations.

3.1 Gauss-Markov Process A simple method for generating a Markov process is by means of the simple recursive formula Xn = pXn-1+ Wn (5) where w, is a sequence of zero-mean independent identically distributed (white) random variables and p is a parameter that determines the degree of correlation between X, and Xn-1 as E[XXn-1] = PE[X?_1] = pon-1 (6) Having wn be Gaussian, we obtain a Gauss-Markov process. (Hint: use randn) H T1 Using MATLAB generate a sequence of 1,000 (equally spaced) samples of a Gauss-Markov process from the recursive relation: Xn = 0.95X -1 + Wn Wn = 1, 2, ..., 1000 (7) H T2 Plot the sequence X, as a function of time index n H T3 Plot the estimate of the auto-correlation for time lag M = 50 given: Rx(m) = N-m Enz" XXatm, m = 1, 2, ..., M N- ml En=/ml+1 XnXn+m, m = -1, -2, ..., -M (8)4. (10 points) Answer the following questions: a. (5 points) What assumptions are required for the Gauss-Markov Theorem to hold? . (5 points) Let , denote some unbiased linear estimator of a regression coefficient , other than the ordinary least squares (OLS) estimator. If the Gauss-Markov Theorem holds, what must be true about B, relative to the OLS estimator B,?5. One of the shortest but most important sections in the book is that on the Gauss-Markov theorem. (a) What is the Gauss-Markov theorem? (b) Carefully explain what the precise properties specified by the Gauss-Markov theorem mean and why they are desirable for an equation. (c) What could cause the Gauss-Markov theorem to no longer hold? What should we do in such a situation?Time sequences: Generate a sequence of 1000 equally spaced samples of a Gauss- Markov process using the recursive relation: Xn = ax- + Wnin = 1,2, ..., 1000. Here assume that Xo = 0, and {w,} is a sequence of independent identically distributed Gaussian random variables. You can use the randn function in MATLAB to generate zero-mean, unit-variance random variables. Below is given a low-pass filter (a>0) excited by a white noise sequence, and the filter has a real pole at z- a. Plot the output waveform for the following values of a: a= 0.5, a = 0.95, a = 0.995. Comment on the effect of the selection of a on the resulting time sequence