You may use one 8.5 11\sheet with notes in you own handwriting on both sides but no other sources of information Calculators are not allowed You may assume all results from lecture, the notes, problem sets, and recitation Write your solutions in the space provided. If you need more space, write on the back of the sheet containing the probl

This is an open-notes exam However, calculators are not allowed You may assume all results from lecture the notes, problem sets and recitation Write your solutions in the space provided. If you need more space, write on the back of the sheet containing the problem Be neat and write legibly. You will be

YOUR NAME Calculators are not allowed on this exam You may use one 8.5 x 11\sheet with notes in your own handwriting on both side but no other sources of information You may assume all results from lecture, the notes, problem sets, and recitation

Problem Set 11 Solutions Due: 5PM on Friday, May 6 This is a mini-problem set. The first problem reviews basic facts about expectation. The second and third are typical final exam questions. Problem 1. Answer the following questions about expectation. (a)There are several equivalent definitions of the expectation of a random variable

Problem Set 10 Solutions Due: Monday, May 2 at 9 PM Problem 1. Justify your answers to the following questions about independence. (a)Suppose that you roll a fair die that has six sides, numbered 1, 2, ... 6. Is the event that the number on top is a multiple of independent of the event that the number on top is a multiple of 3?

Problem Set 9 Solutions Due: Monday, April 25 at 9 PM Problem 1. There are three coins: a penny, nickel, and a quarter. When these coins are flipped: The penny comes up heads with probability 1/3 and tails with probability 2/3 The nickel comes up heads with probability 3/4 and tails with probability 1/4. The quarter comes up heads with

Srini Devadas and Eric Lehman Problem Set 7 Solutions Due: Monday, April 4 at 9 PM Problem 1. Every function has some subset of these properties: injective

Due: Monday, April 11 at 9 PM Problem 1. An electronic toy displays a 4x4 grid of colored squares. At all times, four are red, four are green, four are blue, and four are yellow. For example, here is one possible configuration:

Problem 1. Sammy the Shark is a financial service provider who offers loans on the fol lowing terms. Sammy loans a client m dollars in the morning This puts the client m dollars in debt to Sammy. Each evening, Sammy first charges\service fee\, which increases the client's debt by f dollars, and then Sammy charges interest, which multiplies the debt by a factor

Problem 1. An undirected graph G has width w if the vertices can be arranged in a se- quence V1,2,3,…,Vn such that each vertex v; is joined by an edge to at most w preceding vertices. (Vertex vj precedes if i.) Use induction to prove that every graph with width at most w is (w+1)-colorable