540.305 Quiz 7 (Week 8) Solutions
1. State whether the following statements are true or false, and briefly explain your choice:
a) If we have a PDE whose independent variables are x and t, between x0 and xlast and t0 and tnal , if we
want to known all the
540.305 Probability Models and Distributions
November 4, 2013
1
Probability as the language of statistics
Now when we started I said that probability was the language of statistics.
When we learn probability we often use games as examples, like rolling
540.305 Quiz 2
Solutions
1. Given the following function:
function sequence = produce_sequence(value)
sequence = [value];
for i=1:10
if value = 1
break;
elseif mod(value,2)
value = value*3+1;
else
value = value/2;
end
sequence = [sequence value];
end
what
540.305 Solving Single Nonlinear Equations (Unit 3)
September 12, 2013
Reading : Numerical Methods, Sections 1.1, 1.2, 1.6, 1.7
Introduction to Unit
So the last section concludes our explicit coverage of programming.
For the next few weeks we are going
540.305 Statistics intro - probability
October 31, 2013
Why Statistics?
In the final portion of the class we will cover basic statistics.
I said at the beginning of the course that the ability to solve math problems with a computer is essentially
a huge
Book sections: 6.2, 6.3
Reminder of the central limit theorem's point
So Tuesday I got all excited about the central limit theorem.
Because we could use it to relate our measurements from an experiment to the true mean of what we
are trying to measure.
540.305 Hypothesis Testing
November 21, 2013
Hypothesis testing
Last time in class we talked about techniques to find confidence levels for a series of measurements. That
is, if I give you a set of measurements and a confidence level, you can tell me the
540.305 Quiz 1
Solutions
(
)
1. Write the following in a form that Matlab will evaluate: 4 35 16 .
(For example, 8 6 needs to be written as 8*6.)
4*(3^5-16)
2. Would the following evaluate to TRUE (1) or FALSE (0)?
x = 3;
y = [2 100];
x > y(2)
FALSE - x i
And then we find the probability of drawing a number z standard deviations below the mean using for
example a command in Matlab like alpha = normcdf(p).
that tells us probability that H0 is true.
If is sufficiently small (ie depending on your preferenc
3
Correction to two sample comparison
Last time during lecture I mentioned an approach for calculating the effective number of degrees of freedom for the T distribution that governs the confidence interval for the difference between two samples with
diff
540.305 Quiz 4
Solutions
1. You are trying to use the Newton's method we discussed in class to find the solution to a nonlinear equation
using a Matlab script.
Here is the graph of the function, with the first point marked at x1 , f (x1 ). Find and label
540.305 Quiz 8 (Week 9) answers
1. Let's say you have a random variable X that can take on the value either 1, 6 or 10. P(1) = 0.5, P(6) =
0.3 and P(10) = 0.2.
What is the expectation of X ?
E (X ) =
x
xP(X = x) = 1 0.5 + 6 0.3 + 10 0.2
This is
0.5 + 1.8
540.305Solving Systems of Equations Computationally (Unit
4)
October 2, 2013
Reading : Numerical Methods, Sections 2.1-2.6, 2.8
Effective procedures and programming
So in the last unit we were introduced to the idea of using Matlab to solve equations tha
540.305 Quiz 5
Solutions
1. A separation process is fed with an input stream consisting of 500 kg C2 H5 OH and 500 kg H2 O. The
output consists of two streams. One amounts to a total of 400 kg and contains 96% C2 H5 OH. Your job is
to calculate the mass o
540.305 Quiz 6 (Week 7)
1. This question asks you to apply the forward Euler method to numerically approximate a solution to a
differential equation. In case you don't remember the equations for this method (which is ok, you can always
look them up!), if
Algorithms, or
explaining
complex tasks to
the computer
Rebecca Schulman
September 10, 2013
Summary of what we will cover
this unit
1. Manipulating vectors and
arrays
generating them, accessing them and
reshaping them
2. Repetitive tasks : looping
for and
Fall 2013 540.305 Midterm
1
Calculating Molecular Weight
Your cousin R. Ganic wants to start a drug conpany and has been synthesizing potential drug candidates.
She needs to figure out the molecular weight of her compounds. Write a Matlab function that ta
540.305 Fall 2013 Midterm Review Sheet
General Midterm Information
The 540.305 midterm will be Thursday October 17 in class. It will be 75 minutes - please arrive on time.
The goal of the exam is to test your ability to use Matlab to set up and solve basi
540.305 Quiz 3
Solutions
1. Write the commands for a function that takes two values. first_value and num_values. The function will
produce an array whose first value is first_value and has num_values entries. If the nth entry of this array
is x, then the