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 us what 5 problems to be graded!
1. (20 points) A docto
Important Discrete Distributions
Expectation and Variance
Lecture 17. Bernoulli and Binomial Distributions. Expectation
Discrete Uniform Distribution.
We have seen some examples that all outcomes of an experiment are equally
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 that 1 woman
in 1000 has this cancer. Experience has sho
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 innite and arranged in a 1 dimensional equally-spaced
Lecture 5. Expectation
Probability Density Function: Let f (x) 0 and
P (E ) as following
P (X 2 E ) =
f (x) dx.
f (x) dx = 1. Dene
Are the probability axioms satised?
It is important to observe that there a similar paradox in the calculus
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 =
fBB; BG; GB; GGg, your X could be the number of boys, th
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) =
Let 0 < a < b < 1. Dene
1 if 0 < Ui < a
, and Yi =
1 if 0 < Ui < b
STAT 241/541, Probability Theory with Applications
Harrison H. Zhou (firstname.lastname@example.org)
O ce hours: Wednesday 4:00-6:00pm (tentative) or by appointments, Room
204, 24 Hillhouse Ave., James Dwight Dana House.
Corey Brier <cor