Mathematical Probability, Math 411 - Homework 2 solutions
Problem 1. A person places randomly n letters in to n envelops . What is the probability that
exactly k letters reach their destination.
Solut
Probability Theory, Math 411, Spring 2016 - Homework 1
From the textbook solve the problems 2, 5-10 at the end of the Chapter 1.
And also the problems below:
Problem 1. Show that for any sets A and B
Texas A&M University
Department of Mathematics
Volodymyr Nekrashevych
Fall 2011
Math 411 Problem Set 6
Issued: 10.17
Due: 10.24
6.1. A group of 20 people go out to dinner. 10 go to an Italian restaura
Mathematical Probability, Math 411, Spring 2016 - Homework 10
Problem 1. Show that Almost sure convergence does not imply mean square convergence.
Hint: Let Xn be independent with
1
x = n3
n2
pXn =
.
Probability Theory, Math 411 - Homework 4 solution
Problem 1. Let X be a Binomial random variable with parameters 50 and
0.2. What is the probability of the event that X 5 (you dont have to
simplify t
Mathematicl Probability, Math 411, Spring 2016 - Homework 7 solutions
From the textbook
Solution to Problem 6: Let X be her waiting time then for t > 0
FX (t) = P(X t) = P(X t|no customer in front)P(n
Mathematical Probability, Math 41, sec 504 - Homework 7
Read sections 5.1-5.3.
Solve problems 2,3,7,10,15,16,17 from section 5.6
And also the problems below
Problem 1. Which of the following functions
Texas A&M University Department of Mathematics Volodymyr Nekrashevych
Fall 2011
Math 411 - Problem Set 1 Issued: 09.02 Due: 09.09
1.1. Two dice are rolled. What is the probability that (a) the two num
Texas A&M University
Department of Mathematics
Volodymyr Nekrashevych
Fall 2011
Math 411 Problem Set 2
Issued: 09.09
Due: 09.16
2.1. A bet is said to carry 3 to 1 odds if you win $3 for each $1 you be
Texas A&M University
Department of Mathematics
Volodymyr Nekrashevych
Fall 2011
Math 411 Problem Set 1
Issued: 09.02
Due: 09.09
1.1. Two dice are rolled. What is the probability that (a) the two numbe
Midterm 2 practice, Math 411
1. (10 points) We have a biased coin (probability of heads equal to p). In the first stage
of the experiment we keep tossing it until we get a heads, and we remember how m
Lecture Notes in Probability
Eviatar B. Procaccia
Department of Mathematics
Texas A&M University
Based on lecture notes written by Professor Raz Kupferman,
The Hebrew University of Jerusalem.
April 15
Mathematical Probability, math 411 homework 8 - solutions
Problem 1. Let X be exponentially distributed with parameter . Find
the PMF of Y = dXe, where dxe for a real number x is the rounding of
x to
Probability Theory, Math 411 - Homework 3 solution
Problem 1. The dorm in which you live houses 1% of the total TAMU
student population. You know 30% of the students living in your dorm, but
you know
Mathematical Probability, Math 411 - Homework 6
From the textbook solve the problems 1 and 2 at the end of the Chapter 3.
Solution to Problem 1: The PMF of Y is
P(Y = 1) = P(X 1/3) = 1/3, P(Y = 2) = P
Analysis exercise 4
Sequences of functions
February 5, 2014
Due Wednesday Feb 12.
1. Do problems 9.1 9.9, from the textbook.
The a b symbols means all the questions in the closed interval [a, b]
2. Le
SYLLABUS
"
Mathematical Probability - Math 411
Spring 2016
MWF 9:10-10:00pm, Blocker 149
https:/sites.google.com/site/ebprocaccia/teaching/2016-spring-411
Course Description and Prerequisites
Probabil
Mathematical Probability, Math 411 - Homework 5
From the textbook solve the problems 16, 22, 24 at the end of the Chapter 2.
Solve the problems 5 and 13 from the Chapter 2 additional exercises at
http
Mathematical Probability, Math 411 - Homework 7
Solve the problems 3, 6, 7, 11, 12,16, 17 from the Chapter 3 additional exercises at
http:/www.athenasc.com/prob-supp.html
And also the problems below
P
Mathematical Probability, Math 411 - Homework 9
From the textbook solve the problems 22, 23 and 24 from the Chapter 4.
Solve the problems 21, 22, 24, 30 from the Chapter 4 additional exercises at
http
Mathematical Probability, Math 411, Homework 8
Remember the convolution formula
for the sum of independent random variR
ables Z = X + Y : fZ (z) = fX (x)fY (z x)dx.
From the textbook solve the problem
Mathematical Probability, Math 411, Spring 2016 - Homework 11 (do not hand in)
Problem 1. It is known that among TAMU students 60% support candidate A for the student
council, while only 40% support c
Midterm 1 practice
1. All your HW exercises.
2. (10 points) Suppose a random variable has the following PMF:
PX (k) =
c
,
k2
k cfw_1, 2, 3.
Find c, E[X].
3. (a) (6 points) If = A B, P(A B c ) = 0.6, P
Mathematical Probability Math 411 - Homework 9
Problem 1. Show that for random variables X, Y and Z we have
E[E[E[X|Y ]|Z] = E[X].
Apply this formula to the following problem: Roll a far 6-sided die a
Analysis exercise 3
Continuous functions
January 22, 2014
Due Wednesday Jan 29.
1. Do problems 4.50 4.53, from the textbook.
The a b symbols means all the questions in the closed interval [a, b]
2. Le
Homework 7 (Midterm 2), Math 131B - Winter 2014
Instructor: Eviatar B. Procaccia
P
n
1. (a) Define the radius of convergence of a power series
n=0 an x
(b) What is the interval of convergence for the
1
1. The number of heads is even if it is 0, 2, or 4. It follows that the probability is 32
(1 + 52 +
1+10+5
1
= 16
4 )=
32
32 = 2 .
Another solution: it is clear that the probability is the same as
MATH 411 Sections 200 & 502 - Fall 2016
Homework Assignment 3
Due: Tuesday September 27. In class.
Section and problem numbers are from the course textbook:
D. Bertsekas & J. Tsitsiklis, Introduction
Mathematical Probability, Math 411 - Homework 4
From the textbook solve the problems 16, 22, 24, 26, at the end of the Chapter 2.
Solve the problems 10 and 12, 13 from the Chapter 2 additional exercis
Probability Theory, Math 411 - Homework 11
Problem 1. If X1 , X2 , X3 , . . . is a sequence of of random variables such that E[Xn4 ] converges
to zero, prove that Xn converges in probability to zero.
Midterm 1, Math 411 - Fall 2015
Printed name:
Signed name:
Student ID number:
Instructions:
Read problems very carefully. If you have any questions raise your hand.
The correct final answer alone is
Midterm 2, Math 411 - Fall 2017
Printed name:
The Aggie code of honor:An Aggie does not lie, cheat or steal or tolerate those who do.
Signed name:
Student ID number:
Instructions:
Read problems very
Probability Theory, Math 411 - Homework 4 solution
Problem 1. Let X be a Binomial random variable with parameters 50 and
0.2. What is the probability of the event that X 5 (you dont have to
simplify t