Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
Problem Set #1
Part 1.: Prices  Nominal vs. Real
1. The CPI index has several limitations, one of these is that it does not consider the prices of
services purchased by the government.
True, CPI stands for Consumer Price Index which does not consider the
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
540.305 Problem Set 1 : Matlab Intro / Review
1
Temperature conversion
Write a Matlab function FtoK that takes as an input a temperature in Fahrenheit and outputs the same
temperature in Kelvin. As a reminder, a Fahrenheit temperature f is related to the
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
540.305 Problem Set 5: Solving Nonlinear Equations with
Matlab, Solutions
1
Numbers of solutions
How many solutions do you expect these equations to have? You can use reasoning, graphing, or any other
tools to guess. Note that nonlinear equations may have
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
540.305 Problem Set 6: Numerical Integration and ODE
Solving
1
Numerical Integration Practice
Solve the following ODEs numerically using Matlab's numerical integration tools:
a)
10
e x + e x sin xdx
3
0
xmax = 10;
xmin = 0;
fun = @(x) exp((x.^3) + exp(x
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
540.305 Problem Set 4: Solving Systems of Linear Algebraic
and Ordinary Differential Equations Solutions
1
Solving systems of linear constraint equations with matlab
Solve the following sets of linear equations with Matlab or explain why they cannot be so
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
540.305 Problem Set 9: Measurement Error, Probability
Distributions and the Central Limit Theorem
Part 1 : Suggested Practice Problems
You do not need to hand in anything for this part. This is just a study guide for you, where I recommend practice proble
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
540.305 Problem Set 2 Solutions : Matlab Vectors and Arrays
Note: I am sure many of you have realized that there are many corerect ways to write a program to
perform a particular task. Your goal is to find one. You should always have enough information fr
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
540.305 Problem Set 10 : Confidence intervals, hypothesis
testing, and confidence intervals on the difference between
two means for large samples
Part 1 : Suggested Practice Problems
You do not need to hand in anything for this part. This is just a study
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
540.305 Problem Set 11: Practice (Do not hand in!) for
inferences on the differences in small samples, proportions
and linear regression
Part 1 : Suggested Practice Problems
The answers are in the back of the book for these problems (and for all of the od
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
Dynamics of System Integrated Numerically and Analytically
0.5
Numerical
Analytical
0.48
0.46
0.44
Y
0.42
0.4
0.38
0.36
0.34
0.32
1
1.1
1.2
1.3
1.4
1.5
Time
1.6
1.7
1.8
1.9
2
Optimized Concentration Dependence on Time
10
A
B
P
W
9
8
Concentration [mol/L]
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
Name
aff_tf
aff_ti
barb_tf
barb_ti
comb_z
emp
expected_.
ganador_A
ganador_B
h
i
instances
j
minimo
n
number_i.
otros_cab.
p
P_z
prob4aaa
probabilid.
probabilid.
Ra
Rb
res_3a
st_dev
subtr
sum_varia.
vacio
variance_.
W
z
Value
500
482
495
470
1x11 double
0
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
Distribution of Particle Position
900
800
700
Frequency
600
500
400
300
200
100
0
120
100
80
60
40
20
1D Position [um]
0
20
40
60
3D Trajectory of Particle under Brownian Motion
100
Z Position [um]
80
60
40
20
0
20
50
150
0
100
50
50
0
Y Position
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
540.305 Problem Set 8: Introduction to Probability
Part 1 : Suggested Practice Problems
You do not need to hand in anything for this part. This is just a study guide for you, where I recommend practice problems. They are optional.
The answers are in the b
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
540.305 Problem Set 11: Practice (Do not hand in!) for
inferences on the differences in small samples, proportions
and linear regression
Part 1 : Suggested Practice Problems
The answers are in the back of the book for these problems (and for all of the od
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
1. You are given
p() = Ce
(1)
where 1 = kB T and C is a normalization constant. T is the temperature and kB is
Boltzmanns constant. The energy of an atom can range continuously from 0 to innity
(). Also, by denition of ideality, each atom in the containe
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
Problem 1: We want to fit the data into a straight line mode: yi = a + bxi, and we are
also given these information:
1. The data has Gaussian distributed errors in both x and y coordinates, x = 1,
and y = 2.
2. Assume uniform prior for a and b and, P(a,b
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
I. Atomic Statements (statements that cannot be simplified)
a. Truth (2+2 is 4) (Algebra 2+2 = 4)
b. Not statements (not 2+2, not 4)
II. Compound Statements
a. OR (in algebra => +)
b. AND(in algebra => x)
Ex: if T = 1 ; F=0
1+1 = 1
defined as)
1+0 = 1
0+1
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
CTRL + C stops any search or command
SHG displays plot screen
1) For loop
a. Ex:
function [x] = example(N)
x = 0 (definition)
for i = 1:10:100 (iterate from 1 to 100 in 10s
x = x + i;
end
end
2) If statement => Boolean logic
a. Ex:
function [x] = example
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
Quick Review of Tuesday
 for loops used for repetition;
Ex: x = [ ] (empty array)
For I = 1:1000 (repeat numbers from 1 to 1000)
x(i) = _ (fills in array)
 if statements to establish a condition (if x < or = 0)
 writing functions to recall code(so that
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
Projectile Motion
Modeling and Statistical Analysis for Chemical Engineering
September 22nd, 2011
By:
Elliot Osborne
and
Jorge Marchand
(1) Numerical Integration:
Results:
Riemann sums of f(x) from 01 with varying nmax
The definite integral of the functi
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
Mini Project #3: Frequency analysis, encryption, and decryption
Complete project due: October 30, 2011 (Friday)
Learning objectives:
Mastering Matlab
Manipulating strings, control structure
Reading from and writing to external les
Data analysis
Analy
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
Quiz 2 Answers
September 15, 2011
1. The probability part of the problem was exactly as the languagecognition problem in the
earlier quiz.
Propositions
V Velocity is in [25,26]
V Velocity is not in [25,26], i.e. it is in [26,27]
L Length was greater
Modeling and Statistical Analysis of Data for Chemical and Biomolecular Engineers
CHEMBE 540.305

Fall 2011
Quiz 2 Answers
September 15, 2011
1. Poldrack reported the following frequency table of previous studies that involved any
languagerelated task and whether or not a particular region of interest (ROI) in the brain was
activated.
Language Study Not langua