A factory has produced N televisions for sale. Here N is a Poisson random variable with mean λ. These televisions can fail to function at some time. Assume each television malfunctions independently. Let Xi denote the life time of the ith television produced by this factory, which is a positive random variable that follows an exponential distribution with a rate parameter µ. Let N(t) be the number of televisions which have failed to work by time t.

Submission: Upload your solutions of Exercises 3.1–3.5 to Crowdmark as one PDF file. (Do not hand in any solution to the Supplementary Exercises.) Exercise 3.1. Let P be the transition probability matrix of an irreducible discretetime Markov chain where the state space is E and every state is positive recurrent. Let A be a nonempty, proper subset of E and π be the stationary distribution of P. Given a /∈ E, define E∗ = A ∪ {a} and a new matrix P∗ = (P∗ ij )i,j∈E∗ by

This assignment will help you develop an understanding of ordered lists and basic recursion.

• Your work must be your own. • These problems require thought, but do not require long answers. Please be as concise as possible. • This assignment is due by 2pm on Thursday, October 29. You may use up to two flex days to submit the assignment late, meaning the hard deadline after which no late assignments will be accepted is 2pm Saturday, October 31. • Your assignment must be typed; handwritten assignments will not be marked. You may use any wordprocessing software you like (many academics use LaTeX). Figures can either be drawn electronically, or you may hand-draw, take pictures, and include them as images in your submission. Whatever word-processing you choose, please submit in PDF format. • All assignments must be submitted electronically on MarkUs (see the course webpage for the MarkUs link). Well before the due date, try submitting with MarkUs. You can submit an empty file as a placeholder, and then submit a new version of the file later by using the “Replace” column. Check that you have submitted the correct version of your file by downloading it from MarkUs.

In this assignment, you will be writing programs for generating temporal snapshots of a network and performing basic link analysis of the network. Then, you will work on methods for link prediction in these networks. Furthermore, you will experiment with community detection methods. You will also prepare a technical document where you briefly report about the data, methods, measurements, experiments, and results of the assignment.

The goal of this assignment is to implement a set of classes and interfaces1 to be used to create a simulation of a building management system. You will implement precisely the public and protected items described in the supplied documentation (no extra package-private/public/protected members, methods or classes). Private members and Private methods may be added at your own discretion. • Including extra package-private/public/protected members, methods or classes will cause the compilation for a class to fail, meaning no marks for functionality or unit tests will be awarded for the class. This strictly enforced (because the required specfication has not been followed). As noted below, you should utilise the assignment prechecks to help avoid this. Language requirements: Java version 14, JUnit 4

For this assignment you will be having another look at the record linkage program that you developed in the lab sessions. Specifically, we provide you with two new master data sets from where you need to generate two individual data sets to be used for this assignment. We ask you to work with the programs we have developed in the labs, and provide answers based on your findings. As with the previous assignments, the emphasis is on your understanding, descriptions, and justification as much as the raw (numerical) record linkage evaluation results that you are able to achieve.

In this assignment you will implement path planning algorithms, such as A* and RRT. You will also formulate an LQR problem.

The assignment will be marked with an automatic testing system on Ed as well as manual inspection by a tutor. An mark will be given based on the tests passed (10%) and a mark will be given for overall style, quality, readability, etc (5%). You are expected to write your own tests and submit them with your code, and a mark will be given based on manual inspection of your tests (5%). There will be public test cases made available for you to test against, but there will also be extra non-public tests used for marking. Success with the public tests doesn't guarantee your program will pass the private tests.

The goal of this project is to gain practical experience in applying several database management concepts and techniques using the Oracle DBMS. Your main task is to first populate your database with appropriate data, then design, implement, and test the appropriate queries to perform the tasks explained in the next sections. You must work on this project individually. Academic integrity policies apply. Please refer to 3.60.04 Student Integrity and Misconduct of the University Policy for more information.