18.440 Midterm 2 Solutions, Spring 2011
1. (20 points) Jill polishes her resume and sends it to 900 companies she
nds on monster.com. Each company responds with probability .1
(independently of what all the other companies do). Let R be the number
of comp
Problem 1 (Innite Horizon Problem, 60 points)
An engineer has invented a better mouse trap and is interested in selling it for the right price. At the
beginning of each period, he receives a sale o er that takes one of the values s1 , . . . , sn with corr
18.440 Midterm 2 Solutions, Fall 2011: 50 minutes, 100 points
1. (20 points) Suppose that a fair die is rolled 72000 times. Each roll turns
up a uniformly random member of the set cfw_1, 2, 3, 4, 5, 6 and the rolls are
independent of each other. For each
6.231 Dynamic Programming and Optimal Control
Midterm Exam II, Fall 2011
Prof. Dimitri Bertsekas
Problem 1: (50 points)
Alexei plays a game that starts with a deck consisting of a known number
of black cards and a known number of red cards. At each time p
MIT 2.830/6.780 Problem Set 2 (2008) Solutions
Problem 1
Manyinterestingresponseswerereceived.Wecandiscussonanindividualbasiswhenselectingterm
projects.
Problem 2
Letxbetheconcentrationofparticlesinparticles/ft3:
x ~N(15.08,0.025)
Sincetheacceptableconcen
Massachusetts Institute of Technology
Department of Mechanical Engineering
Department of Electrical Engineering and Computer Science
2.830J/6.780J Control of Manufacturing Processes
Spring 2008
Assignment 1
Out 2/7/2008; due 2/14/2008
The goal of this ass
MIT 2.830/6.780 Problem Set 3 (2008) Solutions
Part 1
Histogramsandnormalprobabilityplotsforintermingledsamplestakenfromtwopopulations,x1~
N(0,1)and x2~N(d,1),forvaluesofdbetween0and4:
Histogram for d = 0
Normal probability plot for d = 0
Frequency
Freque
18.440 Practice Midterm: 50 minutes, 100 points
Carefully and clearly show your work on each problem (without
writing anything that is technically not true) and put a box
around each of your nal computations.
1. (30 points) Twenty people in a room each ha