IEOR E3658
Midterm 1 - Solutions
Fall 2013
Probability: Midterm 1 - Solutions
1. Three dierent machines M1 , M2 and M3 were used for producing a large batch of staplers.
Suppose that 20% of the staplers were produced by machine M1 , 30% by machine M2 and
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Practice Second Midterm
November 7, 2011
Page 1 of 7
Practice Second Midterm
Place all answers on the question sheet provided. The exam is open textbook (Bertsekas and Tsitsiklis)
and open notes/handouts
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Lecture 24
December 6, 2011
Page 1 of 1
Lecture 24
1. Charity University announces a fund raising target of $10 millions. It sends out n letters
to its alumni. From past experience, there is a probabilit
IEOR E3658 HWK 3 - Conditional Probability, Gambler's Ruin (Solutions)
Fall 2013
Prepared by Charles Courtiol ([email protected])
Exercise 1.
PN =
N
N
a Trivially, P0 = 0 and PN = 1. Letting Pn =
= 1. Thus, boundary conditions are veried.
n
N
we have P0
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Assignment #3
September 30, 2015
Page 1 of ?
Assignment #3 due October 7th, 2015
1. We deal from a well-shued 52-card deck. Calculate the probability that the 13th card is the
rst king to be dealt.
2. Ei
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
First Midterm Exam
October 12th, 2011
Page 1 of 8
First Midterm Exam
Place all answers on the question sheet provided. The exam is open textbook (Bertsekas and Tsitsiklis)
and open notes/handouts/homewor
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Assignment #1
September 14, 2015
Page 1 of 2
Assignment #1 due September 23rd, 2015
1. Let A and B be two sets.
(a) Show using Venn diagrams that
Ac = (Ac B) (Ac B c ),
B c = (A B c ) (Ac B c )
(b) Show
IEOR E3658
HWK 8 - 2D CLT, Inequalities
(Solutions)
Fall 2013
Prepared by Charles Courtiol ([email protected])
Exercise 1.
a To compute the marginal distribution we integrate the joint density:
+
s, fX (s) =
fX,Y (s, t)dt
1
2 s2 +4
e 2
=
+
e2t dt
1
2
2
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Practice First Midterm
September 30, 2011
Page 1 of 6
Practice First Midterm
Place all answers on the question sheet provided. The exam is open textbook (Bertsekas and Tsitsiklis)
and open notes/handouts
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Practice Final
December 6, 2011
Page 1 of 17
Practice Final
This Practice Final Exam is intended to be completed in 3 hours and it is worth a
total of 180 points. This examination consists of 17 printed
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Practice First Midterm
October 7, 2011
Page 1 of 6
First Midterm Exam
Place all answers on the question sheet provided. The exam is open textbook (Bertsekas and Tsitsiklis)
and open notes/handouts/homewo
IEOR E3658
HWK 7 - Joint Distributions (continuous) (Solutions)
Fall 2013
Prepared by Charles Courtiol ([email protected])
a The set C = cfw_(X, Y ) : X 2 + Y 2 r2 represents the circle of center (0, 0)
and radius r such that the area enclosed by this
IEOR E3658 HWK 5 - Normal RVs, CLT, Derived Distributions (Solutions)
Fall 2013
Prepared by Charles Courtiol ([email protected])
Exercise 1.
Let X1 , ., Xn independent random variables s.t. Xi N (i , i2 ).
a Using independence of the Xi s we will calcul
IEOR E3658
Practice Midterm 1 - Solutions
Fall 2013
Probability: Practice Midterm 1 - Solutions
October, 2013
Name:
UNI:
Instructions
Please write your answers on the question sheets. Answers written on scrap paper will not
be evaluated. Show and explain
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Assignment #7
October 26, 2011
Page 1 of 2
Assignment #7 due November 2nd, 2011
1. Consider a random variable X that takes values in the interval (0, a) whose density function
has a triangular shape and
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Course Information
September 6, 2011
Page 1 of 2
Course Information
Course Description
This is an introductory course in probability designed to develop a good understanding of uncertain
phenomena and th
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Assignment #3
September 27, 2011
Page 1 of 2
Assignment #3 due October 5th, 2011
1. (From text) We deal from a well-shued 52-card deck. Calculate the probability that the
13th card is the rst king to be
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Assignment #2
September 26, 2015
Page 1 of 2
Assignment #2 due September 30th, 2015
1. Stans birthday is approaching. He thinks that there is a 0.6 chance that his wife will get
him a new pair of red sus
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Assignment #10
November 17, 2011
Page 1 of 1
Assignment #10 due November 23rd, 2011
1. (From text) If X is a random variable that is uniformly distributed between -1 and 1, nd
the PDF of |X | and the PDF
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Assignment #4
October 4, 2011
Page 1 of 2
Assignment #4 due October 12th, 2008
1. The annual premium of a special kind of insurance starts at $1000 and is reduced by 10%
after each year where no claim ha
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Assignment #8
November 2, 2011
Page 1 of 1
Assignment #8 due November 9th, 2011
1. The time Andrew will be at the dentist has an exponential distribution with mean of one hour.
He comes to a parking mete
IEOR 3658
Probability
Rouba Ibrahim
Midterm #2
November 16, 2009
Solutions to Midterm #2
1. (20 points) Suppose that the joint probability mass function of random variables X and Y is
given by
0.5
0.1
0.1
pX,Y (x, y ) =
0.2
0.1
0
if X = 1 and
if X = 1 and
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Assignment #7 Solutions
November 13, 2011
Page 1 of 3
Assignment #7 Solutions
1. (a) Since b < 0 and shape of the density is triangular, bx + c has to have a x-intercept of a
and an area of one. The heig
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Assignment #5
October 12, 2011
Page 1 of 2
Assignment #5 due October 19th, 2010
1. (From text) A stock market trader buys 100 shares of stock A and 200 shares of stock B.
Let X and Y be the price changes
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Assignment #4 Solutions
October 7, 2011
Page 1 of 2
Assignment #4 Solutions
1. Let S =$1000, r=0.1, p=0.05. Then the PMF of the total premium paid up to and including
the rst claim year is:
PX (x) = (1 p
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Assignment #3 Solutions
October 10, 2011
Page 1 of 2
Assignment #3 Solutions
1. The number of ways to deal 13 out of total 52 cards is (52 P 13). For the case of rst king
being the 13th card, there are (
IEOR 3658
Probability
Prof. Mariana Olvera-Cravioto
Assignment #2
September 21, 2011
Page 1 of 2
Assignment #2 due September 28th, 2011
1. You have 3 coins in your pocket that are undistinguishable to the touch; two of them are
normal coins, the other one
Probability Class 5
*
Next quiz cheat sheet allowed
- quiz only covers material up to the Wednesday that the HW was assigned
*
If A and B are independent events
P(A BC) = P(A) P(A B) = (because A and B are independent) P(A) P(A)P(B)
= P(A)(1-P(B) = P(A)P(