MATH 464
HOMEWORK 7
SPRING 2013
The following assignment is to be turned in on
Thursday, March 28, 2013.
1. Consider the following experiment: Roll 2 fair, four sided dice. Consider
the following discrete random variables:
X = the number of odd dice.
Y =
MATH 464
HOMEWORK 3
SPRING 2013
The following assignment is to be turned in on
Thursday, February 7, 2013.
1. Three couples are invited to a dinner party. They will independently
show up with probabilities 0.9, 0.8, and 0.75 respectively. Let N be the
num
MATH 464
HOMEWORK 1
SPRING 2013
The following assignment is to be turned in on
Thursday, January 24th, 2013.
1. Let A, B, and C be events (subsets) of a sample space .
Write each of the following events in terms of A, B, and C using intersections, unions,
MATH 464
HOMEWORK 2
SPRING 2013
The following assignment is to be turned in on
Thursday, January 31, 2013.
1. Suppose we pick a letter at random from the word MISSISSIPPI. Write
down a sample space and give the probability of each outcome?
2. In a group o
> # hmwk5_r.txt
>
> # p is probability of heads
> p=0.25;
> X<-0
> Y<-0
> SquareX<-0
> SquareY<-0
>
> for (n in 1:100000) cfw_
+
+ # seq is used to record the flips
+ seq=as.character();
+
Math 464 - Fall 13 - Homework 4
1. We roll a six-sided die n times. Each time the die comes up 1, we ip a
fair coin. Let X be the number of heads we get. Note that the number of
times the coin is ipped is random. Find the mean and variance of X.
2. You ha
# hmwk5_r.txt
> # p is probability of heads
> p=0.25;
> X<-0
> Y<-0
> SquareX<-0
> SquareY<-0
>
> for (n in 1:100000) cfw_
+
# seq is used to record the flips
+
seq=as.character();
+
# flip until we get H
+
count1<-0;
+
got_head<-0;
+
while (got_head=0) c
Math 464 - Fall 13 - Homework 2
1. In the 1990s the ELISA test was used to test blood donations for the
AIDS virus. If a sample of blood has the virus, the test will be positive
99.9% of the time. If the sample does not have the virus the test will be
neg
MATH 464
HOMEWORK 4
SPRING 2013
The following assignment is to be turned in on
Thursday, February 14, 2013.
1. Let X be a discrete random variable on a probability space (, F, P ).
Let g : R R be a function and set Y = g(X), i.e. Y : R is dened by
Y () =
MATH 464
HOMEWORK 6
SPRING 2013
The following assignment is to be turned in on
Thursday, March 7, 2013.
1. Suppose that in a certain state the license plates have three letters followed by 3 numbers. If no letter or number can be repeated, how many
licens
MATH 464
HOMEWORK 5
SPRING 2013
The following assignment is to be turned in on
Thursday, February 21, 2013.
1. Let x, y R and take n 2 an integer. Prove that
n
(x + y)n =
k=0
n k nk
x y
k
using an induction argument.
2. Let X be a binomial random variable
MATH 464
HOMEWORK 8
SPRING 2013
The following assignment is to be turned in on
Thursday, April 4, 2013.
1. Let X be a Poisson random variable with parameter > 0.
a) Find the moment generating function for X.
b) Use your result above to nd the mean of the
MATH 464:
TEST 2
MAKE UP
SPRING 2013
Name
I.D. Number
Question
Points Score
1
10
2
10
3
10
4
10
5
10
6
10
7
10
Total
70
1
2
SPRING 2013
Rules to the Make-Up:
Here are the rules to the make-up. You have two choices. Either you
turn in the make-up, or you d
6
Jointly continuous random variables
Again, we deviate from the order in the book for this chapter, so the subsections in this chapter do not correspond to those in the text.
6.1
Joint density functions
Recall that X is continuous if there is a function
5
Continuous random variables
We deviate from the order in the book for this chapter, so the subsections in
this chapter do not correspond to those in the text.
5.1
Densities of continuous random variable
Recall that in general a random variable X is a fu
Solutions for Exam 2 - Math 464 - Fall 11 -Kennedy Show your work! Correct answers with no work get no points. 1. (16 points) Let X be a random variable with the uniform distribution on [-2, 2]. Let Y = X 2 . (a) Find the probability density function (pdf
Final Exam Solutons - Math 464 - Fall 2011 1. I roll two tetrahedral (four-sided) dice. Let X be the number of dice that show an odd number, Y the number that show an even number. So both X and Y only take on the values 0, 1, 2. (a) Find the joint probabi
Final Exam Review Problem Solutions - Math 464 - 2011 1. An urn has 1 red ball and 2 green balls. I draw a ball. If if it is red, I put it back in the urn. If it is green I do not put it back. Then I draw a second ball. (a) Find the probability the second
Final Exam Review problems - Math 464 - Fall 2011 1. An urn has 1 red ball and 2 green balls. I draw a ball. If it is red, I put it back in the urn. If it is green I do not put it back. Then I draw a second ball. (a) Find the probability the second ball i
Review questions for Exam 1 - Solutions Math 464 - Fall 11 1. Let X be a discrete RV with a Poisson distribution whose mean is 3. (a) Find P(X 1|X 2). Since the mean is 3, the parameter = 3. P(X 1|X 2) = P(1 X 2) P(X = 1) + P(X = 2) = P(X 2) P(X = 0) + P(
Review questions for Exam 1 - Math 464 - Fall 11 -Kennedy These questions are meant to be representative of the questions that will be on the exam. However, if a topic does not appear here that does not mean it will not appear on the exam. These ten probl
Sample Exam 2 Solutions - Math 464 - Fall 10 -Kennedy 1. Let X have a gamma distribution with = 2, w = 3. Let Y = 3X. Show that Y has a gamma distribution and find the values of and w for Y . (Hint: how is the moment generating function of Y related to th
Sample Exam 2 - Math 464 - Fall 11 -Kennedy The questions on this sample exam are meant to be representative of the questions that will be on the exam. However, if a topic does not appear on the sample exam that does not mean it will not appear on the exa
Homework 1
Due September 6
Problems 1.20, 1.26, 1.30 from the textbook
Add-on sketch of a proof of existence of a set which is not Lebesgue-measurable. The original example is due to G. Vitali. Let = [0, 1); we will show that there is no translation-invar
Final Exam Review problems - Math 464 - Fall 2013
1. An urn has 1 red ball and 2 green balls. I draw a ball. If it is red, I put
it back in the urn. If it is green I do not put it back. Then I draw a second
ball.
(a) Find the probability the second ball i