ORIE 3500/5500, Fall 2016, Practice Midterm 2
Practice Midterm Exam (50 mins)
DISCLAIMER: This is a practice exam and will
not be identical to actual midterm exam.
However, you can learn the types of questions
that I will ask from this exam. Solutions wil
ORIE 3500/5500, Fall 2016, Practice Midterm 1
Practice Midterm Exam (50 mins)
DISCLAIMER: This is a practice exam and will
not be identical to actual midterm exam.
However, you can learn the types of questions
that I will ask from this exam. Solutions wil
ORIE 3500/5500, Fall 2016, Homework 8
Homework 8: Due November 5th at 5pm
Problem 1. Let X and Y be the coordinates of a point selected at random
inside the triangle
T = cfw_(x, y) | y 0, y 1 + x, y 1 x.
That is, the joint pdf of X and Y is
(
fX,Y (X, Y )
ORIE 3500/5500, Fall 2016, Homework 7
Homework 7
Solutions
Problem 1. If X Gamma(n, 1), how large should n be so that
)
(
X
P 1 > 0.01 < 0.01
n
a) according to Chebyshevs inequality?
Solution:
a) Since E(X/n) = 1, by Chebyshevs inequality we have:
)
(
X
V
ORIE 3500/5500, Fall 2016, Homework 5
Homework 5
Solutions
Problem 1. Let X and Y be two independent random variables, where X
has a Bernoulli distribution with probability of success p = 1/2 and Y has a
Bernoulli distribution with probability of success
ORIE 3500/5500, Fall 2016, Homework 8
Homework 8: Due November 5th at 5pm
Problem 1. Let X and Y be the coordinates of a point selected at random
inside the triangle
T = cfw_(x, y) | y 0, y 1 + x, y 1 x.
That is, the joint pdf of X and Y is
(
fX,Y (X, Y )
ORIE 3500/5500, Fall 2016, Homework 3
Homework 3 Due September 23rd
Problem 1. Let pi = P (X = i). and
a) Suppose that p1 + p2 + p3 = 1. If EX = 2, what values of p1 , p2 and p3 (i)
maximize and (ii) minimize Var(X)?
b) Suppose now that p1 + p2 + p3 + p4
ORIE 3500/5500, Fall 2016, Homework 2
Homework 2
Solutions
Problem 1. Suppose that the waiting time (in minutes) to be served at a
counter in a bank is a continuous random variable X having the density function
if x < 0,
0
fX (x) = 1/2
if 0 x < 1,
3/(2x4
ORIE 3500/5500, Fall 2016, Homework 1
Homework 1
Solutions
Problem 1. Five cards are selected from a 52-card deck for a poker hand.
Find the probability of the following poker hands.
a) Four of a kind. This is, four cards of the same denomination and any
ORIE 3500/5500, Fall 2016, Homework 6
Homework 6 Due October 21st
Read Chapter 11 of the textbook.
Problem 1. Exercise 11.1 in textbook.
Problem 2. Exercise 11.2 in textbook.
Problem 3. A continuous random variable X has a Pareto distribution with
paramet
ORIE 3500/5500, Fall 2016, Homework 1
Homework 1 Due September 2nd
Reading :
What Are The Odds? (Article on Blackboard)
Read Chapters 1 and 2 of the textbook.
Problem 1. Five cards are selected from a 52-card deck for a poker hand.
Find the probability of
ORIE 3500/5500, Fall 2016, Homework 2
Homework 2 Due September 16th
Reading :
Read Chapters 3 and 4 of the textbook.
Problem 1. Suppose that the waiting time (in minutes) to be served at a
counter in a bank is a continuous random variable X having the den
ORIE 3500/5500, Fall 2016, Homework 5
Homework 5 Due October 14th
Problem 1. Let X and Y be two independent random variables, where X
has a Bernoulli distribution with probability of success p = 1/2 and Y has a
Bernoulli distribution with probability of s
ORIE 3500/5500, Fall 2016, Homework 4
Homework 4 Due September 30th
Problem 1.
Let X and Y be independent standard normal random variables, that is,
they both have probability density function given by
t2
1
fX (t) = fY (t) = e 2 , t R.
2
Let U = X + Y and
ORIE 3500/5500, Fall 2016, Homework 7
Homework 7 Due October 28th
Read Chapter 8 and Re-read Chapter 11 of the textbook.
Problem 1. If X Gamma(n, 1), how large should n be so that
X
P 1 > 0.01 < 0.01
n
a) according to Chebyshevs inequality?
Problem 2.
Y?
ORIE 3120
Homework #8
Due May 4, 2016
Please include a printout of relevant R output for each problem.
Problem 1. Logistic analysis in R. First, enter the data in the file castdata.csv:
cast = read.csv("castdata.csv",header=TRUE)
attach(cast)
Examine the
Decision Making under Uncertainty
Simulation decisions in the presence of uncertainty.
Why not plug in the expected values of the random variables?
Example
You pick two people from a large population at random and
compute the ratio between the ages of
1. Random Variables
Suppose we are to perform a random experiment whose
outcome cannot be predicted in advance.
The set of all possible outcomes of the random experiment is
called the sample space.
1. If the experiment is tossing a die,
2. If the experi
1. Random Variables
Suppose we are to perform a random experiment whose
outcome cannot be predicted in advance.
The set of all possible outcomes of the random experiment is
called the sample space.
1. If the experiment is tossing a die,
2. If the experi