Name:
Midterm Exam
1. For the function
each)
g (x )=
x 2 + x+3
x 21
find the following:
(5 points
a. Horizontal asymptote(s) (if any)
b. Vertical asymptote(s) (if any)
If there are not any, please explicitly state this. Otherwise, be sure to give the
equa
Name:
Assignment 3  Solution
Each problem in this homework is worth 10 points unless otherwise
indicated.
1. When social security numbers in the US contain were originally given
out, the following format was used in order to help assign them (before
the
Name:
Assignment 5 Solutions
1. A couple decides to have children until they have a boy. Lets assume
that they are able to continue to do so and each time they conceive,
they only have a single child (no twins or triplets, etc.). (a is worth 4
points and
Name:
Assignment 1  Solutions
f ( x )=9 x1
1. Prove that
points)
is onetoone function.
(10
Assume that f(x1) = f(x2)
f(x1) = 9x1  1
f(x2) = 9x2  1
9x1  1 = 9x2  1
9x1 = 9x2
x1 = x2
Since x 1=x2 follows from the assumption that f ( x 1 )=f ( x 2) ,
Module 3
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Module 3
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Module 1
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Name:
Assignment 6
1. Find
,
,
E ( X ) Var ( X ) ( X )
function
f (x)
if a random variable
X
is given by its density
, such that
(25
points)
f ( x )=0 , if x 0
f ( x )=6 ( xx 2) , if 0< x 1
f ( x )=0 , if x> 1
1
1
1
1


6
6
6
6
6
6
6 6 24 18
xf ( x ) dx
Name:
Assignment 2  Solutions
1. For the function
part)
f ( x )=
x 3 3 x2
4 x+ 10 find the following: (10 points for each
3
2
a. Horizontal or vertical asymptotes, if any. If there are not any, please
explicitly state this. Otherwise, be sure to give the
Name:
Assignment 4 Solutions
1. During an experiment, a card is selected at random from a standard
deck of 52 cards. Event A is getting a red card. Which of the following
events are independent of event A?
(Each part is worth
3 points)
a) The card selecte
The basic rules of Differentiation of functions in calculus are presented along with several
examples.
1  Derivative of a constant function.
The derivative of f(x) = c where c is a constant is given by
f '(x) = 0
Example
f(x) =  10 , then f '(x) = 0
2 
Complementary Material (4 of 4)
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Complementary Material (4 of 4)
Attachment 4
Area under the standard normal curve from 0 to X
(source: http:/www.statsoft.com/textbook/sttable.html (http:/www.statsoft.com/textbook/sttable.html) )
0.00
0.01
Mathematical
Expectation, E(X)
Variance, Var(X)
Standard deviation
Probability
Probability Distributions
Geometric
Normal
E(X)=1/p
xf ( x ) dx
E(X)=
Binomial
E(X) = np
Var(X) = npq = np(1p)
Var(x) =
p
(1 p)2
Always equal to
1. If n is large and
p0.10 the
Module 6
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Module 4
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PURDUE QUANTITATIVE FINANCE CLUB
Presents
Rolando D. Navarro, Jr.
Ph.D. Candidate, Department of Statistics
Computational Finance Program
Purdue University
navarror@purdue.edu
Banking Experience
Risk Analyst (20102011)
Standard Chartered Bank
Group Model