University of Illinois
Fall 2009
ECE 313: Problem Set 4: Solutions Counting Random Variables, Maximum-Likelihood Estimation
1. [Graphical study of binomial pmfs] (a) Work out the numbers yourself. (b) The graphs are as shown below.
0.4 0.2 0 0 1 2 3 4 5 6
University of Illinois
Fall 2014
ECE 313 (Section X)
Homework 10
Due Date: Thursday, November 6, 08:00 AM in the class
Write your name and NetID on top of all the pages. Show your work to get partial credit.
Problem 1 Remember the following properties for
University of Illinois
Fall 2014
ECE 313 (Section X)
Homework 10 Solution
Problem 1
a) A valid hazard function h(t) (or z(t) should satisfy the properties in the second column
of the table shown above:
() should be defined for all positive time, 0 <
()
ECE 313 - Section X
Midterm Exam Solution
Fall 2014
Name: _
NetID: _
Be sure that your exam booklet has 10 pages.
Write your name at the top of each page.
This is a closed book exam.
You may consult both sides of your single 8.5" x 11" sheet of notes.
No
Probability with Engineering Applications
ECE 313 Course Notes
Bruce Hajek
Department of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
August 2014
c 2014 by Bruce Hajek
All rights reserved. Permission is hereby given to fr
University of Illinois
ECE 313: Final Exam
Fall 2014
Monday, December 15, 2014, 7:00 p.m. 10:00 p.m.
Sect. B, names A-O, 1013 ECE, names P-Z, 1015 ECE; Section C, names A-L, 1015 ECE; all others 112 Gregory
1. (a) On the average, it takes 6 rolls until th
University of Illinois
Fall 2014
ECE 313: Hour Exam II
Wednesday, November 12, 2014
7:00 p.m. 8:15 p.m.
Sect. B in 151 Everitt Lab, Sects. C&E in 100 Noyes Lab, Sect. D in 1404 Siebel Center
1. [24 points] (6 points) Suppose X is a random variable with th
University of Illinois
Fall 2014
ECE 313: Hour Exam II
Wednesday, November 12, 2014
7:00 p.m. 8:15 p.m.
Sect. B in 151 Everitt Lab, Sects. C&E in 100 Noyes Lab, Sect. D in 1404 Siebel Center
1. (a) Note that fX (u) = 0.5 for u [0, 1] [2, 3] because the pd
University of Illinois
ECE 313: Conict Final Exam
Fall 2014
Tuesday, December 16, 2014, 7:00 p.m. 10:00 p.m. Room 2013 ECE Building
1. (a) Let c denote the fraction of nonsmoking women who get lung cancer (over some time
period). Then 13c is the fraction
University of Illinois
Fall 2014
ECE 313: Hour Exam I
Wednesday, October 8, 2014
7:00 p.m. 8:15 p.m.
Section B in 151 Everitt Lab, Sections C & E in 141 Loomis Lab, Section D in 100 MSEB
1. [14 points] Suppose n solar cells are in a linear array, in posit
University of Illinois
Summer 2014
ECE 313: Exam I
Monday, July 7, 2014
7:00 p.m. 8:15 p.m.
269 Everitt Lab
1. [12 points] Guessing Restaurant Quality: Suppose you go to a restaurant and do not
know the restaurant quality beforehand. Assume the restaurant
University of Illinois
Summer 2014
ECE 313: Exam I
Monday, July 7, 2014
7:00 p.m. 8:15 p.m.
269 Everitt Lab
1. (a) Let L denote the restaurant quality level. Then P[L = ] = 1 for = 1, . . . , 5. Let
5
Y denote the Poisson distribution with mean 10 for = 1
University of Illinois
Summer 2014
ECE 313: Exam II
Thursday, July 24, 2014
7:00 p.m. 8:15 p.m.
269 Everitt Lab
1. [10 points] Suppose X has the binomial distribution Bin(n, 1 ) for some n 1.
2
(a) (6 points) Use the Gaussian approximation to nd an approx
University of Illinois
Fall 2014
ECE 313: Hour Exam I
Wednesday, October 8, 2014
7:00 p.m. 8:15 p.m.
Section B in 151 Everitt Lab, Sections C & E in 141 Loomis Lab, Section D in 100 MSEB
1. [14 points] Suppose n solar cells are in a linear array, in posit
University of Illinois
Fall 2014
ECE 313: Hour Exam I
Wednesday, October 8, 2014
7:00 p.m. 8:15 p.m.
Section B in 151 Everitt Lab, Sections C & E in 141 Loomis Lab, Section D in 100 MSEB
1. (a) There are n possibilities for which two cells fail, and n 1 p
Lecture3
TheGroundwork
Discreterandomvariables
Conditionalprobability
A
AB
Mostlylanguage
Language
Outcome: Head(H),orTail(T)
Samplespace():setofallpossibleoutcomes:H,T
Itsfair ifP(H)=P(T)=
Event:asubsetof
P(cfw_H)=P(H)= (Hisbothanoutcomeandanevent)
P
University of Illinois
Fall 2016
ECE 313: Exam II
Wednesday, November 9, 2016
8:45 p.m. 10:00 p.m.
A-C will go to room ECEB 1013
D-I will go to room ECEB 1015
J-Z will go to room ECEB 1002
Name: (in BLOCK CAPITALS)
NetID:
Signature:
Section:
2 A, 9:00 a.m
University of Illinois
Spring 2016
ECE 313: Exam II
Wednesday, April 13, 2016
7:00 p.m. 8:15 p.m.
Aa-Hs in DCL 1320,
Ht-Lf in ECEB 1013,
Lg-Np in ECEB 1015,
Nq-Zz in ECEB 1002
Name: (in BLOCK CAPITALS)
NetID:
Signature:
Section:
2 E, 9:00 a.m.
2 C, 10:00
University of Illinois
Fall 2016
ECE 313: Exam II
Wednesday, November 9, 2016
8:45 p.m. 10:00 p.m.
A-C will go to room ECEB 1013
D-I will go to room ECEB 1015
J-Z will go to room ECEB 1002
1. [20 points] Let X be a random variable with CDF given by
C1
u <
University of Illinois
Spring 2016
ECE 313: Exam II
Wednesday, April 13, 2016
7:00 p.m. 8:15 p.m.
Aa-Hs in DCL 1320,
Ht-Lf in ECEB 1013,
Lg-Np in ECEB 1015,
Nq-Zz in ECEB 1002
1. [10 points] Consider the CDF in the figure below.
1.0
0.75
0.5
1
2
2.5
Car
University of Illinois
Fall 2016
ECE 313 (Section F)
Homework 3 Solution
Problem 1
Given that occurrence of different kinds of defects are independent from each
other, we have:
= + + + ()
= 0.05 + 0.08 + 0.1 0.05*0.08 0.0
University of Illinois
Fall 2016
ECE 313 (Section X)
Homework 5
Due Date: Wednesday, October 5, 11:00 AM in the class
Write your name and NetID on top of all the pages. Show your work to get partial credit.
Problem 1 Suppose two fair dice are rolled. Let
University of Illinois
Fall 2016
ECE 313 (Section X)
Homework 1 Solution
Problem 1
a) We enter 16 times to the for loop, and in each look entry we have 2 possible cases based on
the value of variable p:
Sample space consists of (2)16 combinations of A
University of Illinois
Spring 2008
ECE 313: Problem Set 1
Calculus Tune-up
Due:
Reading:
Wednesday January 23 at the beginning of class.
Ross, Chapters 1 and 2
This Problem Set contains five problems
Note: Most of the topics covered on this problem set wi
The Erlang distribution is a two parameter family of continuous probability distributions with
support
. The two parameters are:
a positive integer 'shape'
a positive real 'rate'
; sometimes the scale
The Erlang distribution with shape parameter
, the inv
University of Illinois
Spring 2008
ECE 313: Problem Set 2
Due:
Reading:
Wednesday January 30 at the beginning of class.
Ross, Chapters 1 and 2
This Problem Set contains seven problems
1. Consider events O and G pertaining to the outcome of the presidentia
1/21/2017
Lecture2
Poker
Poker
Fullhouse
Straight
Whowins?
1/21/2017
Poker
Fullhouse
Straight
Whydoesfullhousewin?
Poker
P(Fullhouse)=?
P(Straight)=?
1/21/2017
Ourplan
1.
2.
3.
4.
Language
Equallylikelyoutcomes
Principleofcounting
Principleofovercou
Occurrence[edit]
Applications of the Poisson distribution can be found in many fields related to counting:[29]
Telecommunication example: telephone calls arriving in a system.
Astronomy example: photons arriving at a telescope.
Biology example: the number