Stat 241/541 Final Exam
12/17/2012, 2:00-4:30PM. This is a two-hour-and-a-half exam for which you
have three hours.
Important: You may choose 5 out of the following 6 problems to
work on. Please tell
Week 7
Important Discrete Distributions
Expectation and Variance
Lecture 17. Bernoulli and Binomial Distributions. Expectation
Revisited.
Discrete Uniform Distribution.
We have seen some examples that
Week 4
Lecture 8. Discrete conditional distribution.
Examples 1: A doctor gives a patient a test for a particular cancer. Before
the results of the test, the only evidence the doctor has to go on is t
Week 6
Lecture 14
Random Walks
Drunkard Walk. Imagine now a drunkard walking randomly in an ideals
ized 1 dimensional city ( or 2 dimensional, or 3 and higher dimensional city).
The city is eectively
Week 3
Lecture 5. Expectation
Probability Density Function: Let f (x) 0 and
P (E ) as following
Z
P (X 2 E ) =
f (x) dx.
R
f (x) dx = 1. Dene
E
Are the probability axioms satised?
It is important to o
Week 2
Lecture 3. Expectation and Probability axioms.
Random variable. A random variable is a real-valued function dened on
the sample space, i.e., X (! ) is a function from to R. For example, for =
f
Midterm Exam, 2012 Fall (Time: 9:00-10:15am, Oct. 19)
1. Let U1 ; U2 ; : : : ; Un be i.i.d. from U [0; 1], each with density function
f (x) =
1
0
0<x<1
.
otherwise
Let 0 < a < b < 1. Dene
Xi =
1 if 0
Homework 2
Due September 13.
Chapter 2.2: 2, 4, 6, 8, 12.
Problem 6: Let X
U (0; 1).
(i) Find the density of Y = 1=X and EY .
X
(ii) Find the density of Y = tan 2 and EY .
1
STAT 241/541, Probability Theory with Applications
Fall 2013
Instructor:
Harrison H. Zhou ([email protected])
O ce hours: Wednesday 4:00-6:00pm (tentative) or by appointments, Room
204, 24 Hillhous