Mathematics Department, UCLA T. Richthammer
winter 09, nal Mar 02, 2009
Final: Math 170A Probability, Sec. 1
1. (6 pts) Consider a probability model with S = cfw_1, 2, 3, 4, P (cfw_1, 2) = 1 , P (cfw_1, 3) = 1 . 2 4 (a) Is it possible that P (cfw_4) = 0?
Probability Theory, Math 170a, Homework 1
From the textbook solve the problems 2, 510 at the end of the Chapter 1.
And also the problems below:
Problem 1. Show that for any sets A and B
P(A B) P(A) P(A B).
Problem 2. You want to buy a car on a certain we
Probability Theory, Math 170A,  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
And also the problems below:
Problem 1. Recall Problem form Hom
4.1 Introduction
CHAPTER 4
Probability
While the graphical and numerical methods of Chapters 2 and 3 provide us
with tools for summarizing data, probability theory, the subject of this chapter,
provides a foundation for developing statistical theory. Most
Probability Theory, Math 170A,  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:/www.athenasc.com/probsupp.html
And also the problems be
Math 170A Fall 2013
Homework 7
Suggested reading:
Review Chapters I, II, Sections 3.1 and 3.2 from Chapter III and Sections 4.2 and 4.3 from Chapter
IV for the midterm.
The solutions to Problem 3 and 9 at the end of Chapter II.
Problems:
(1) Solve probl
Mathematics Department, UCLA T. Richthammer
winter 09, sheet 5 Jan 30, 2009
Homework assignments: Math 170A Probability, Sec. 1
051. An apartment complex is equipped with an alarm system that is supposed to directly give alarm at a police station if there
Mathematics Department, UCLA T. Richthammer
winter 09, sheet 10 Mar 06, 2009
Homework assignments: Math 170A Probability, Sec. 1
120. Express the following probabilities in terms of the joint CDF F of X = (X1 , X2 ): (a) P (X1 a, X2 > b) Answer: (a) P (X1
Mathematics Department, UCLA T. Richthammer
winter 09, sheet 1 Jan 02, 2009
Homework assignments: Math 170A Probability, Sec. 1
001. Let E1 , E2 , . . . be subsets of a universal set S . Draw Venn diagrams for the following sets: (a) E1 E2 E3 , (d) E1 Ans
MATH 170A, PROBABILITY THEORY, WINTER 2016
STEVEN HEILMAN
Abstract. These notes closely follow the book of Bertsekas and Tsitsiklis, available here.
Contents
1. Introduction
2. Sets and Probabilities
2.1. Sets
2.2. Probabilistic Models
2.3. Conditional Pr
Chapter 1 Problems
(1) Let S, T, U and S1 , S2 , . . . be sets. Prove that
c
(a) S (T U ) = (S T ) (S U ),
(b)
Si
c
Si .
=
i=1
i=1
(2) Before the early 1990s, a telephone area code in the US consisted of three digits, where the rst
was not 0 or 1, the sec
Final practice, Math 170A  Fall 2015
Instructor: Martin Tassy
Name and student ID:
Question
Points
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
9
10
10
10
Total:
100
Score
1. (a) (2 points) Let A and B be events such that P(A B) = P(A B) = 1/2. Find P(A).
Sol
Probability Theory 170A
Steven Heilman
Please provide complete and wellwritten solutions to the following exercises.
Due March 10, in the discussion section.
Homework 8
Exercise 1. Let X be a continuous random variable with distribution function fX (x) =
Linear Algebra, Math 170A, Fall 2015, Lec 1  Course Info
Instructor: Martin Tassy, 5117 Math Sciences Building, mtassy@math.ucla.edu,
Instructor Oce Hours: MWF 1011am in 6909 Science Building
Lectures: Monday, Wednesday and Friday, 33:50pm in 6229 Math
Probability Theory, Math 170A, Fall 2015  Homework 9
From the textbook solve the problems 18, 20, 22, 25, 34 from the Chapter 3.
Solve the problems 10, 12, 15, 17 from the Chapter 3 additional exercises at
http:/www.athenasc.com/probsupp.html
And also t
Probability Theory, Math 170A,  Homework 8, DUE MONDAY NOVEMBER 30
From the textbook solve the problems 6, 7, 11 and 15 at the end of the Chapter 3.
Solve the problems 3, 6, 7, 8 and 14 from the Chapter 3 additional exercises at
http:/www.athenasc.com/pr
Math 170A Winter 2013
Homework 4
(1) Read sections 2.2, 2.3 and 2.4 from the book. Also: nish reading the excerpt from Silvers book.
(2) Solve problems 1 and 6 from the end of chapter II.
(3) Solve problems 1 through 5 from the Practice midterm (posted on
Probability Theory, Math 170A, Fall 2015 2015, Homework 3
From the textbook solve the problems 17, 23,24,27,30 at the end of the
Chapter 1.
And also the problems below:
Problem 1. If a day is sunny the probability that the next day will be rainy
is 1/2. I
Probability Theory, Math 170A,  Homework 6
From the textbook solve the problems 25,26,31,32 at the end of the Chapter 2.
Solve the problems 12,14, 15 ,16 from the Chapter 2 additional exercises at:
http:/www.athenasc.com/probsupp.html
And also the probl
Probability Theory, Math 170A,  Homework 7
From the textbook solve the problems 1 and 2 at the end of the Chapter 3.
And also the problems below:
Problem 1. If X and Y are independent random variables and E(X) = 0 show that
E(X Y )2 ) = E(X + Y )2 ).
Doe
Probability Theory, Math 170a, Homework 2
Solve the problems 49,50,51,52,53,56,58,60 from the Chapter 1
And also the problems below:
Problem 1. Assume that 0 m n. Give a combinatorial proof that
n
m
n
=
k=m
k1
.
m1
(Hint: how many melement subsets of cfw
Probability Theory, Math 170A, Fall 2015, Homework 4
From the textbook solve the problems 3 to 7 at the end of the Chapter 2.
And also the problems below:
Problem 1. In a certain soccer tournament you are playing once with each
of the other nine teams. In
Topology/Metric Spaces
1
Before we begin
d(x, z) = x z = x y + y z =
(x y) + (y z) x y + y z =
d(x, y) + d(y, z)
Before we discuss topological spaces in their full generality, we will rst turn our attention to a special type of
On
the
plane
R2
Final practice, Math 170A  Fall 2015
Instructor: Martin Tassy
Name and student ID:
Question
Points
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
9
10
10
10
Total:
100
Score
1. (a) (2 points) Let A and B be events such that P(A B) = P(A B) = 1/2. Find P(A).
(b)
Some useful formulas.
PMF of Bernouli (p):
pX (1) = p, pX (0) = 1 p.
Expectation is p, variance is p(1 p).
PMF of Bin(n, p):
n k
p (1 p)1k , for k = 0, 1, 2, , n.
pX (k) =
k
Expectation is np. Variance is np(1 p).
PMF of Geo(p):
pX (k) = (1 p)k1 p, f
Probability Theory 170A
Steven Heilman
Please provide complete and wellwritten solutions to the following exercises.
Due January 7th, in the discussion section.
(This Review Assignment will be collected but not be graded.)
Preliminary Review Assignment
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Math 170A Quiz 1 19 January
Total score: 12 points
Full name: ljl g2 YCE E Q 9 Cl! 0?le (1 point)
1. (3 points) Let A, B and C be sets. Which of the following statements must be true?
I. A(BC)= (AmB)n(AnC)
II. AU(BUC)C= (AUBC) (AUCC)
III. AU(AnB) AUB
AOlI
Math 170A Quiz 3 . 25 October
Total score: 15 points
Full name: I l Gt'rgb 8 Q 9d 5 hwc 30 (1 point)
1. (4 points) Let X be the number of times a fair six sided dice needs to be rolled in order to get
1 or2. Thean(3SX35) =
ODIH 0.9114 oohI
+
A
_
l
Dolll
Math 170A  Homework 2  Due 26 January 2017
For questions 1 to 9, no justification needed; your final answers are enough. For questions 10
and 11, show all your work.
1. Two fair six sided dice are rolled.
(i) What is the probability that the minimum of