1
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= e^(-1) delta(t-1) t=1
a.s.
SLLN
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When we count from the smallest element, as n tends to infinity the probability that the middle element will be 1 tends to 1,
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EE 122 1st Term Exam
Date: October 9, 2002
Name:
SID:
ee122 login:
Day/time of section you attend:
Problem
1
2
3
4
5
6
Total
Points
/10
/10
/20
/20
/20
/20
/100
1. Question 1 (10 pt)
Use no more than three sentences to answer the questions below:
(a) Stat

EECS 126, Final, Fall 2000
EECS 126, Fall 2000
Final
Professor Chang-Hasnain
Problem #1 (15 points)
X and Y are independent Gaussian random variables with zero mean and unit variance.
Z=X/(X+Y). Find the pdf of Z.
Problem #2 (10 points)
X and Y are indepe

Department of EECS - University of California at Berkeley
EECS 126 - Probability and Random Processes - Spring 2007
Midterm 2: 4/19/2007
SOLUTIONS
1. (25%)
Let X, Y, Z be i.i.d. N(0, 1).
a) Show that X + Y and (X Y )2 are independent;
b) Calculate E[X + Y

Department of EECS - University of California at Berkeley
EECS126 - Probability and Random Processes - Spring 2000
Midterm No. 1: 2/23/2000
Name and SID:
Answer the questions on these four sheets. Show your work. Good luck.
Problem 1: (25%) You ip a fair

Department of EECS - University of California at Berkeley
EECS 126 - Probability and Random Processes - Fall 2008
Midterm 1: 10/09/2008
Name:
SID:
1. Short Questions (20%); 4% each
1.1. Define Random Variable
1.2. Complete the sentence: A, B, C are mutual

Name: _
Student ID No: _
UNIVERSITY OF CALIFORNIA
College of Engineering
Department of Electrical Engineering and
Computer Sciences
Professor Ren
Fall 1997
EECS 126 MIDTERM #2
November 17, 1997, Monday 7-9 p.m.
[42 pts.] 1. Given the joint probability den

EECS 126 Probability and Random Processes
Kannan Ramchandran
University of California, Berkeley: Fall 2014
September 23, 2014
Midterm Exam 1
Last name
First name
SID
Rules.
DO NOT open the exam until instructed to do so.
Note that the test has 105 point

EE 126, Midterm #2, Fall 2001
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EE 126, Fall 2001
Midterm #2
Professor Anantharam
The exams starts at 3:40 p.m. sharp and ends at 5:00 p.m. sharp.
There are 5 problems. The maximum score

EECS 126
EECS 126 - MIDTERM # 1 Professor Ren
October 9 , 1997, Thursday 6-8 p.m.
[15 pts.] 2. A committee of four is picked randomly from a pool of 5 men and 4 women. Find the
probability that there will be more women than men on the committee.
[25 pts ]

EE122 Spring 2001 Final
EE122 Spring 2001 Final
1: True or False [20%]
1. Light in a fiber travels faster than signals in copper.
2. Block coding can achieve a higher compression than Huffman codes.
3. Layer 2 switching cannot be used for a large network

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EECS 104, Spring 1992
Midterm #2
Professors Leon Chua & Ernest Kuh
(NOTE: Greek letters are sometimes written in Roman alphabet in all caps. Subscripts are written A_1,
etc. Micro is sometimes represented by a 'u'.)

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UC Berkeley
Department of Electrical Engineering and Computer Sciences
EE126: Probability and Random Process
Midterm 1 Solution
Fall 2014
Problem 1. (a) The size of the sample space is the number of different ways that
52 objects can be divided in 4 group

EE 117
ELECTROMAGNETIC FIELDS AND WAVES
2/26/14
Midterm Examination 1
Spring 2014
Prof. C. Chang-Hasnain
If you need additional conditions to solve a problem, please write down your assumptions.
Answer in the space below the problem. If you need additiona

Department of EECS - University of California at Berkeley
EECS 126 - Probability and Random Processes - Spring 2007
Midterm 2: 4/03/2007
SOLUTIONS
1. (20%)
The random variables X, Y are independent. X is uniformly distributed in [0, 1] and Y is exponentia

Midterm 2 Solutions
EE126 - Fall 2000
Problem 1.
X Y unif (;1 1)
Z = XY
Let U = X and V = XY and form the jacobian for fUV (u v).
f = 1 f (u v=u)
jU j
UV
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Marginalize with respect to u and employ the independence of X and Y.
fV (v) = fZ (z ) =
fZ (z ) =

EE122, Midterm #1, Spring 1997
EE 122 - Spring 1997
Midterm #1 - 15 % of course grade
March 12, 1997
(closed book)
1) Multiple Choice & Why (17 possible points)
In this problem, you are to select which of the multiple choices are most correct or most appr

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EE122 - Midterm 1 Examination
EECS-UC Berkeley
October 2000
B
This is a closed book exam. The paper consists of 7 pages including the cover
page. THe total poin obtinable for the paper is 100. Students are required to
answer all questions. Write

EECS 126 Probability and Random Processes
Kannan Ramchandran
University of California, Berkeley: Fall 2015
September 22, 2015
Midterm Exam 1 Solution
Last name
First name
SID
Name of student on your left:
Name of student on your right:
DO NOT open the ex

EECS 126 Probability and Random Processes University of California, Berkeley: Spring 2015
Abhay Parekh
February 17, 2015
Midterm Exam
Last name
First name
SID
Rules.
You have 80 mins (5:10pm - 6:30pm) to complete this exam.
The exam is not open book, bu

Department of EECS - University of California at Berkeley
EECS 126 - Probability and Random Processes - Spring 2007
Midterm 1: 2/19/2007
1. (10%)
You are given a 1-meter long wood stick. You choose two points A and B uniformly and independently on the sti

EECS 126 MIDTERM #1
1. Suppose there exists a test for cancer with the following properties. Let
A = event that the test states that the tested person has cancer.
B = event that person has cancer.
P ( B ) = 0.005
P ( A B ) = 0.95
c
c
It is known that P (

Midterm Exam 1 Solutions
1)
P (AjB ) = a P (B ) = b P (B c jAc ) = e
P (B jA) = P (AjPB()A)P (B ) = Pab
(A)
c
c
P (A) = P (AjB )P (B ) + P (AjB )P (B ) = ab + P (AjB c )(1 ; b)
P (AjB c ) = 1 ; P (Ac jB c )
c c
c
P (Ac jB c ) = P (B PjA(B)cP) (A ) = e(1 1

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Electrical Engineering 118
Spring 2001 Midterm 1
Professor Gustafson
Problem #1 (30 points)
A plane wave travels through a right-angle glass prism as shown. The prism materials has an index of
refraction which depends upon frequency (w = 2*pi*f)

EECS 126 Probability and Random Processes
Kannan Ramchandran
University of California, Berkeley: Fall 2015
September 22, 2015
Midterm Exam 1
Last name
First name
SID
Name of student on your left:
Name of student on your right:
DO NOT open the exam until

UNIVERSITY OF CALIFORNIA
College of Engineering
Department of Electrical Engineering and
Computer Sciences
Professor Tse
Fall 1998
EECS 126 MIDTERM #1 Solutions
1a. (i) E, F independent
P ( E F ) = P ( E ) = 0.4 .
P( E F)
(ii) E, F mutually exclusive P (

EE122, Spring 99, Midterm 1
EE122 Midterm Exam
UC Berkeley, Spring 1999
Problem 1: (10 points)
(a)(1) briefly define time-division multiplexing (TDM) and statistical multiplexing
(b)(2) assume 4 data sources each have a peak rate p and mean rate m. They a

EE 126 Probability and Random Processes
Kannan Ramchandran
University of California, Berkeley: Fall 2015
EE 126 Probability and Random Processes: Course Syllabus
1
Administrative Info
Instructor: Prof. Kannan Ramchandran, 269 Cory Hall, kannanr@eecs.berk