Name: SOLUTIONS
MassachusettsInstituteofTechnology
DepartmentofMechanicalEngineering
DepartmentofElectricalEngineeringandComputerScience
2.830J/6.780J Control of Manufacturing Processes
Spring2008
Quiz#1
ThursdayMarch13,2008
In all problems, please show y
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 5
Out 3/11/2008; due Thursday 3/20/2008
Part 1
May
6.231 Dynamic Programming
Midterm, Fall 2009
Problem 1
(30 points)
An enterprising nancier dreams of making it big in the currency market. He may trade between n currencies
c1 , . . . , cn and can convert a unit of ci to rij units of cj , for any currency
Name: _
MassachusettsInstituteofTechnology
DepartmentofMechanicalEngineering
DepartmentofElectricalEngineeringandComputerScience
2.830J/6.780J Control of Manufacturing Processes
Spring2008
Quiz#1
ThursdayMarch13,2008
In all problems, please show your work
6.231 Dynamic Programming and Optimal Control
Midterm Exam, Fall 2011
Prof. Dimitri Bertsekas
Problem 1: (50 points)
Alexei plays a game that starts with a deck with b black cards and r red
cards. Alexie knows b and r. At each time period he draws a rando
MIT 6.780J 2008: Problem set 8 solutions
Problem 1: example solution courtesy of M. Imani Nejad
a) first we calculate the averages and then use the formula in May and Spanos to find b and b 0 :
x=
y=
1 n
yi =
n i=1
=
(x x)(y y) = 2397.779 = 0.96601
2482
18.440 Practice Midterm 2 Partial Solutions
1. (20 points) Let X and Y be independent Poisson random variables with
parameter 1. Compute the following. (Give a correct formula involving
sums does not need to be in closed form.)
(a) The probability mass fu
MIT 2.830/6.780 Problem Set 6 (2008) Solutions
Problem 1
See the following pages for exemplary solutions (courtesy X. Su and K. Umeda)
For the t-test part of the question, two approaches were accepted: one in which the
significance of each effect was test
o~G^GzG 2008
G
wGXGOXYTXWPG
OPG
Factorial Fit: Color versus Solv/React, Cat/React, .
Estimated Effects and Coefficients for Color (coded units)
Term
Effect
Coef
Constant
2.7700
Solv/React
1.4350
Cat/React
0.7175
-1.4650 -0.7325
Temp
-0.2725 -0.1363
React
18.440 Practice Final Exam: 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. This practice exam
deals only with the portion of the c
Solution to Midterm 6.231 2009 Fall
Problem 1
(a) We consider a completely connected directed graph consisting of n nodes (each represents a currency).
The length of an arc from i to j is aij = ln rij . Now we consider the shortest path problem from some