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
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
Linear Algebra, Math 170A, Fall 2015, Lec 1 - Course Info
Instructor: Martin Tassy, 5117 Math Sciences Building, [email protected],
Instructor Oce Hours: MWF 10-11am in 6909 Science Building
Lectures: Monday, Wednesday and Friday, 3-3:50pm 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/prob-supp.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
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 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/prob-supp.html
And also the problems be
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 m-element 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
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)
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, 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/prob-supp.html
And also the probl
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
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 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
P(A B) P(A) P(A B).
Problem 2. You want to buy a car on a certain we
Homework 3
Name:
, UID:
, Discussion section:
July 13, 2015
Please use this as a cover sheet.
The due date of this homework is 7/16.
Solve the following problems from the textbook.
p. 123 : 21, 22, 26, Read 27 and 33.
Additionally, solve the following pro
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
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
Math 115, Fall 2012
Practice Final December , 2012
Total possible points: 220
1. (10 point) Prove (2 + 2)1/2 is irrational.
2. (30 points) Decide (with proof) whether the following series converge.
1.
2.
3.
1
n=2 n2 n
n
2n
1
(1)n cos n
3. (30) poins) Let
Chapter 3: Joint Distributions
1
Introduction
This chapter is concerned with the joint probability structure of two or more random variables dened
on the same sample space.
In ecological studies, counts of several species, modeled as random variables, ar
Midterm 1, Math 170a - Lec 3, Fall 2012
Instructor: Toni Antunovi
c
c
Printed name:
Signed name:
Student ID number:
Instructions:
Read problems very carefully. If you have any questions raise your hand.
The correct nal answer alone is not sucient for fu
Midterm 1 practice, Math 170a - Lec 3, Fall 2012
Instructor: Toni Antunovi
c
c
Name and student ID:
Question
Points
1
12
2
10
3
10
4
10
5
8
Total:
50
Score
1. (a) (6 points) If = A B , P(A B c ) = 0.6, P(Ac B ) = 0.2 nd the probabilities of A and B .
Solu
Probability Theory, Math 170a, Winter 2015, Toni Antunovi c
c
Homework 1
From the textbook solve the problems 2 and 10 at the end of the Chapter
1.
Solve the problems 1, 2, 3 and 5 from the Chapter 1 additional exercises at
http:/www.athenasc.com/prob-sup
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
Math 170A Winter 2013
Homework 1
(1) Study sections 1.1, 1.2 and 1.3 and the solutions to problems 3, 4 and 12 at the end of the chapter.
(2) Solve the following problems from the end of Chapter I: 7, 9, 10, 14 and 16.
(3) A coin is ipped 3 times. How man
Math 170A Winter 2013
Homework 3
(1) Read sections 1.5 and 1.6 (again!), and the scans from Nate Silvers book.
(2) Solve the following problems from the end of chapter I: 52, 53, 54, 49 and 55.
(3) How many ways can 8 people be seated in a row, if
(a) The
Math 170A Winter 2013
Homework 2
(1) Read sections 1.4, 1.5, 1.6 and the solutions to problems 13 and 47 at the end of the chapter.
(2) Solve the following problems from the end of chapter I: 17, 33, 40, 49 and 50.
(3) Two fair six sided dice are rolled,