Handout D Challenges to Solving Probability Problems
There are many things to think about when solving a probability problem, including: Establish the UniverseSample Space Establish outcomes ( experiments ! sample space) Establish the events in the
Introduction to Probability and Statistics for Electrical Engineering
EE 364

Fall 2014
Example 1
In your summer internship, you are working for the worlds largest producer of light bulbs.
Your manager asks you to estimate the quality of production, that is, to estimate the
probability that a bulb produced by the factory is defectless. You
Introduction to Probability and Statistics for Electrical Engineering
EE 364

Fall 2014
EE364 FALL 2014: M IDTERM S OLUTIONS
Oct. 9, 2014
P ROBLEM 1 (5+5+5+15+10=40 pts): Circle the correct answer below
(a) Is the following statement TRUE or FALSE?
P (A1 A2 A3 An1 An )
= P (A1 ) P (A2 A1 ) P (A3 A1 A2 ) P (An A1 A2 A3 An1 )
(b) A wellshu
J. M. Mendel Spring 2010
EE 364 Midterm # 2
Closed Book Two 81/2X11 sheet of notes (both sides) permitted Calculator required Tables A.1, A.2 and A.3 required To receive full credit you must carry out all of the numerics
x
1. (20 points) For parts a and b
Introduction to Probability and Statistics for Electrical Engineering
EE 364

Spring 2016
Practice Problem Set 1
1. Consider the experiment of tossing a fair coin repeatedly and counting the number of tosses
required until the first head appears.
a. Find the sample space of the experiment.
b. Find the probability that the first head appears on
Introduction to Probability and Statistics for Electrical Engineering
EE 364

Spring 2016
Practice Problem Set 2
1. A box contains 3 blue and 2 red marbles while another box contains 2 blue and 5 red
marbles. A marble drawn at random from one of the boxes turns out to be blue. What is the
probability that it came from the first box?
2. A poker
Introduction to Probability and Statistics for Electrical Engineering
EE 364

Spring 2016
Discussion # 3. Outline
Additive Rules
Conditional Probability
Understanding language used in Probability
Sampling with and without replacement
Symmetry (handout)
TA Roberto Slide 1
Discussion # 3. Additive Rules
Corollary 2.2 if 1 , 2 , , are mutually
ex
Introduction to Probability and Statistics for Electrical Engineering
EE 364

Spring 2016
Slide 1
Discussion # 2. Outline
Counting Rules:
Multiplication
Permutation
Combination
Probability of events
Counting Rules
They provide a mathematical way to enumerate the number of ways that a certain outcome can occur.
Counting is relevant to obtain pr
Introduction to Probability and Statistics for Electrical Engineering
EE 364

Spring 2016
Discussion # 5. Outline
TA Roberto Slide 1
The Monty Hall problem
Random Variables
Probability Distributions:
Probability Mass Function, (PMF), for discrete random variables.
Probability Density Function, (PDF), for continuous random variables
Cumulative
Introduction to Probability and Statistics for Electrical Engineering
EE 364

Spring 2016
Discussion # 4. Outline
Symmetries handout (Follow up)
Mutually Exclusive vs Independence
Total Probability
Bayes Rule
Total probability and the Bayes Rule
TA Roberto Slide 1
Discussion # 4. Symmetries (follow up)
TA Roberto Slide 2
Each position in the d
Introduction to Probability and Statistics for Electrical Engineering
EE 364

Spring 2016
Lecture 4: Probability3
1. Additive Rules: We now step to the next level of complexityS and multiple
events.
a. Fact 1: Multiple events are combined using logical connectors.
b. Fact 2: We associate the word OR with the inclusive OR, i.e., with the
union
Introduction to Probability and Statistics for Electrical Engineering
EE 364

Spring 2016
Lecture 9: Random Variables and Probability Distributions3
g. Density and Distribution Calculations (Continued)
ii. Given f (x) find F(x) : IntegrationYou may need cases to compute
F(x) . Cases means that f (x) changes as x sweeps from
to
.
h. Warning: H
Introduction to Probability and Statistics for Electrical Engineering
EE 364

Spring 2016
Lecture 7: Probability6/Random Variables and Probability
Distributions1
Probability6
1. Bayess Rule
a. Theorem 2.14: If the events B1, B2 ,., Bk constitute a partition of the
sample space S, where P ( Bi ) 0, for i = 1,2,.,k , then for any event A of
S
Introduction to Probability and Statistics for Electrical Engineering
EE 364

Spring 2016
Lecture 5: Probability4
1. Additive Rules (Continued):
a. Many times it is much more difficult to calculate the probability that an
event occurs then it is to calculate the probability that the event does not
occur. In such cases:
i. Find P(A) .
ii. Comp
Introduction to Probability and Statistics for Electrical Engineering
EE 364

Spring 2016
Discussion # 6. Midterm # 1 Review
TA Roberto Slide 1
Midterm # 1 will be held on Thursday, February 18th
Time: 2:00 3:20 pm (at usual class time for section 30541)
12:30 1:50 pm (at usual class time for section 30889)
Location: ZHS 252 (usual classroom f
Introduction to Probability and Statistics for Electrical Engineering
EE 364

Spring 2016
Discussion # 1
TA (section 30541): Roberto Martin del Campo Vera
Office hours: Wed 56 pm, Thu 3:304:30 pm
Office: EEB 303
Email: mart737@usc.edu
Slide 1
Outline
Definition of Probability
Random Experiment
Sample Space
Event
Tree diagrams
Set Theory
Sli
Introduction to Probability and Statistics for Electrical Engineering
EE 364

Spring 2016
Lecture 10: Random Variables and Probability Distributions4
1. Joint Probability Distributions (Continued)
a. Joint Probability Distribution for Discrete Random Variables:
i. Definition 3.8: The function f (x, y) is a joint probability distribution or
pr
Introduction to Probability and Statistics for Electrical Engineering
EE 364

Spring 2016
EE 364 Homework 1
In Walpole et al., do the following exercises:
Sec 2.2 (pp. 4244): 2.2, 2.6, 2.12, 2.16, 2.18
Sec 2.3 (pp. 5152): 2.28, 2.32, 2.36
In addition, do the problems below:
Problem 1: Suppose you flip a coin repeatedly until you get heads. Y
Introduction to Probability and Statistics for Electrical Engineering
EE 364

Spring 2016
EE 364 Homework 4
In Walpole et al., do the following exercises:
Sec 2.6 (pp. 6971): 2.76, 2.94
Sec 2.7 (pp. 7677): 2.102 (Assume that the host knows which door you picked and
which door the prize was behind, and always opens a door that you didnt pick