170B Practice Midterm Solution
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Signature:
August 20, 2015
Instructions
This is a 110-minute closed-book exam. The textbook, lecture notes, and all personal scratch papers
are
Math 170B - Probability Theory, Lec.1, Winter 2016 - Homework 2
Due: Thursday, Jan. 21st 2016, at the beginning of discussion.
From the books supplementary problems, solve problems 15, 16, 17, 30, 31, 32
in Chapter 4 (see http:/www.athenasc.com/prob-supp.
170B Final Practice Set
Name:
, UID:
,
I read, understood, and will follow the instructions given below.
Signature:
September 10, 2015
Instructions
This is a 110-minute closed-book exam. The textbook, lecture notes, and all personal scratch papers
are not
Probability Theory, Math 170B - Homework 6
From the textbook solve the problems 4 and 5 from the Chapter 5.
Solve the problems 6, 7, 9, 10 and 18 a) c) d) e) and 19 from the Chapter 7 additional exercises
at
http:/www.athenasc.com/prob-supp.html
And also
Math 170B - Probability Theory, Lec.1, Fall 2015 - Homework 2
Due: Wednesday, Oct. 7th 2015, at the beginning of class.
From the books supplementary problems, solve problems 15, 16, 17, 30, 31, 32
in Chapter 4 (see http:/www.athenasc.com/prob-supp.html).
MATH 170B
Instructor: Sungjin Kim, MS 6617A, E-mail: i707107@math.ucla.edu
Meeting Time and Location: MWR 9:00 - 10:50 AM, Room: MS 5117
Oce Hours: MWR 11:00 AM - 12:30 PM, Room: MS 6617A
Discussion Session: Miller Stephen, T 9:00 - 10:50 AM, Room: MS 511
170B Final Practice Set
Name:
, UID:
,
I read, understood, and will follow the instructions given below.
Signature:
September 10, 2015
Instructions
This is a 110-minute closed-book exam. The textbook, lecture notes, and all personal scratch papers
are not
170B Practice Midterm
Name:
, UID:
,
I read, understood, and will follow the instructions given below.
Signature:
August 20, 2015
Instructions
This is a 110-minute closed-book exam. The textbook, lecture notes, and all personal scratch papers
are not allo
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Probability Theory, Math 170B, Winter 2016 - Homework 5
Extra problems:
Problem 1. (a) Show that if
| maxcfw_0, a maxcfw_0, b| > 0
then
|a b| .
(b) Show that if Xn X in probability then maxcfw_0, Xn maxcfw_0, X in
probability.
Problem 2. Let x and y be t
Math 170B - Probability Theory, Lec.1, Fall 2015 - Homework 8
Due: Friday, Nov. 20th 2015, at the beginning of class.
From the textbook, solve problems 1, 2 and 3 at the end of Chapter 6.
From the books supplementary problems, solve problems 3, 6 (a), (b)
Math 170B
Midterm 2
November 20
Answer the questions in the spaces provided on the question sheets. If you
run out of room for an answer, continue on the back of the page. Explain
your answers and reasoning.
Name:
ID number:
Name that you would like to be
Midterm 1, Math 170B - Winter 2016
Printed name:
Signed name:
Student ID number:
(By signing here, I certify that I have taken this test while refraining from cheating.)
Instructions:
If you are found cheating, your exam will receive zero credit.
When t
Useful formulas.
o PMF 0f Bernouli (p): pX(1) = p,pX(0) = p.
Expectation is p, variance is p(1 p).
o PMF 0f Bin(n,p):
Expectation is np. Variance is np(1 p).
o PMF of Geo(p):
1 1
Expectation is . Variance is 2 .
p p p
o PMF 0f P0i()\):
Ak
pX(k) : 6)H for
T. Liggett
Mathematics 170B Midterm 2 Solutions
May 23, 2012
(20) 1. (a) State Markovs inequality.
Solution: If X 0, then P (X a) EX/a for a > 0.
(b) Prove Markovs inequality.
Solution: a1cfw_Xa X. Taking expected values gives aP (X a) EX.
(c) Suppose X i
Math 170B - Probability Theory, Lec.1, Fall 2015 - Homework 5
Due: Wednesday, Oct. 28th 2015, at the beginning of class.
From the textbook, solve problems 4 and 5 at the end of Chapter 5. Moreover,
work through problem 2 (Chernov bound) which is solved in
Convergence of random variables
In this note, we explain the three different definitions of convergence of
random variables.
Let X1 , X2 , be a sequence of random variables which come from the
same experiment, that is, they are all functions from the same
Probability Theory, Math 170B, Winter 2016 - Homework 1
Extra problems:
Problem 1. Suppose that X1 and X2 are two independent exponential
random variables with parameters 1 and 2 respectively.
(a) What is the law of min(X1 , X2 )? (that is, find the PDF a
Math 170B - Probability Theory, Lec.1, Fall 2015 - Homework 7
Due: Friday(!), Nov. 13th 2015, at the beginning of class.
From the books supplementary problems, solve problems 18 (a), (c), (d), (e) and
19 in Chapter 7 (see http:/www.athenasc.com/prob-supp.