STAT302: Introduction to Probability
Fall 2014-15
Assignment 1
Due date: see course website (Under Schedule).
Instructions
Academic integrity policy: I encourage you to discuss verbally with other students about the assignment.
However, you should write y
Worked examples Random Processes
Example 1 Consider patients coming to a doctors oce at random points in time. Let
Xn denote the time (in hrs) that the nth patient has to wait before being admitted to see
the doctor.
(a) Describe the random process Xn , n
Lesson 20
Probability and Cumulative
Distribution Functions
Recall
If p(x) is a density function for some characteristic of a
population, then
Recall
If p(x) is a density function for some characteristic of a
population, then
We also know that for any den
CHAPTER 4: Poisson Processes
(part 1)
In this chapter, we deal with stochastic process that has continuous time and discrete state space.
Examples are
1. X(t) = The number of telephone calls in time (0 t];
2. Y (t) = the number of trac accidents at certai
http:/www.stat.ubc.ca/~bouchard/courses/stat302-fa2014-15/
Intro to Probability
Instructor: Alexandre Bouchard
Fall 2014
Thursday, October 30, 14
Plan for today
The uniform and exponential
distributions, continued
Poisson processes
Thursday, October 30,
http:/www.stat.ubc.ca/~bouchard/courses/stat302-fa2014-15/
Intro to Probability
Instructor: Alexandre Bouchard
Fall 2014
Saturday, October 18, 14
Webwork
No webwork this week
I have opened the solution of Webwork 6 if
you want to see more problems on th
http:/www.stat.ubc.ca/~bouchard/courses/stat302-fa2014-15/
Intro to Probability
Instructor: Alexandre Bouchard
Fall 2014
Wednesday, October 29, 14
Plan for today
Introduction to continuous
distributions
Distribution of the function of a
random variable
http:/www.stat.ubc.ca/~bouchard/courses/stat302-fa2014-15/
Intro to Probability
Instructor: Alexandre Bouchard
Fall 2014
Friday, October 3, 14
Plan for today
Important shortcuts when computing
expectations
Variance
Friday, October 3, 14
http:/www.stat.u
http:/www.stat.ubc.ca/~bouchard/courses/stat302-fa2014-15/
Intro to Probability
Instructor: Alexandre Bouchard
Fall 2014
Tuesday, October 14, 14
http:/www.stat.ubc.ca/~bouchard/courses/stat302-fa2014-15/
Announcements
Assignment 2 (new deadline)
Webwork
Chap 3: Two Random Variables
Chap 3 : Two Random Variables
Chap 3.1: Distribution Functions of Two RVs
In many experiments, the observations are expressible not as a single quantity, but as a family
of quantities. For example to record the height and weig
http:/www.stat.ubc.ca/~bouchard/courses/stat302-fa2014-15/
Intro to Probability
Instructor: Alexandre Bouchard
Fall 2014
Friday, November 7, 14
Webwork
New webwork release: Wed Nov 5th, 5pm,
due exactly one week later
Friday, November 7, 14
Plan for toda
http:/www.stat.ubc.ca/~bouchard/courses/stat302-fa2014-15/
Intro to Probability
Instructor: Alexandre Bouchard
Fall 2014
Monday, November 24, 14
Plan for today
Conditioning, continued
Law of total expectation
Law of total variance
Monday, November 24,
http:/www.stat.ubc.ca/~bouchard/courses/stat302-fa2014-15/
Intro to Probability
Instructor: Alexandre Bouchard
Fall 2014
Friday, November 21, 14
Plan for today
Conditioning, continued
Law of total expectation
Law of total variance
Friday, November 21,
http:/www.stat.ubc.ca/~bouchard/courses/stat302-fa2014-15/
Intro to Probability
Instructor: Alexandre Bouchard
Fall 2014
Monday, October 27, 14
Plan for today
Introduction to continuous
distributions
Distribution of the function of a
random variable
Ex
http:/www.stat.ubc.ca/~bouchard/courses/stat302-fa2014-15/
Intro to Probability
Instructor: Alexandre Bouchard
Fall 2014
Thursday, October 23, 14
Info on midterm
BRING A SCIENTIFIC CALCULATOR
See Midterm study resources under Tools tab of website:
Wednesd
Winter 2014 STAT 302
Chapter 1 Combinatorial Analysis
Learning outcomes:
Aim: Demonstrate the ability to solve combinatorial problems
Use the basic principle of counting to obtain the total number of
possible outcomes in a random experiment
Differentiat
Winter 2014 STAT 302
Chapter 2 Axioms of Probability
Learning outcomes:
Aim: Demonstrate an understanding of basic probability concepts
Recognize the random experiment of interest in a given scenario
List all possible outcomes in the sample space of a r
http:/www.stat.ubc.ca/~bouchard/courses/stat302-fa2014-15/
Intro to Probability
Instructor: Alexandre Bouchard
Fall 2014
Wednesday, October 15, 14
Webwork
No webwork this week
I have opened the solution of Webwork 6 if
you want to see more problems on t
http:/www.stat.ubc.ca/~bouchard/courses/stat302-fa2014-15/
Intro to Probability
Instructor: Alexandre Bouchard
Fall 2014
Thursday, October 9, 14
http:/www.stat.ubc.ca/~bouchard/courses/stat302-fa2014-15/
Announcement
New assignment posted
Webwork due Fr
1. The joint probability function of X and Y is given as:
X
P(X = x, Y = y)
2
1
0.05
2
0.25
3
0.15
Y
4
6
0.14 0.1
0.10 0.02
0.17 0.02
(a) Find P(XY 6).
A. 0.56
B. 0.69
C. 0.14
D. 0.44
(b) X and Y have a correlation coecient of 2 , and Var(X) = 1, Var(Y )
1. (a) B
(b) A
(c) B
2. A
3. (a) A
(b) C
(c) D
(d) D
4. (a) A
(b) C
5. (a) X Bin(10, 0.5) and Y Bin(20, 0.5). Z = Y X Bin(10, 0.5). The random
variable Z is independent of X and Y. Also, X|Y = 12 Hypergeom(N = 20, n =
10, m = 12).
P (Y = 12, X = 6)
P (Y =
STAT302: Introduction to Probability
Fall 2014-15
Assignment 1
Due date: see course website (Under Schedule).
Instructions
Academic integrity policy: I encourage you to discuss verbally with other students about the assignment.
However, you should write y
STAT302: Introduction to Probability
Fall 2014-15
Assignment 2
Due date: see course website (Under Schedule).
Instructions
Academic integrity policy: I encourage you to discuss verbally with other students about the assignment.
However, you should write y
1. (a) E (b) A
2. B
3. (a) C (b) A (c) A (d) C
4. D
5.
1
Practice Final A
0.5
yaxis
1.0
Question 5 Part I
The area we are interested in is enclosed in the gure below, where the light gray shade represents
the square [0, 1][0, 1], and the darker area repre
STAT302: Introduction to Probability
Fall 2014-15
Assignment 4
Due date: see course website (Under Schedule).
Instructions
Academic integrity policy: I encourage you to discuss verbally with other students about the assignment.
However, you should write y
STAT302: Introduction to Probability
Fall 2014-15
Assignment 2
Due date: see course website (Under Schedule).
Instructions
Academic integrity policy: I encourage you to discuss verbally with other students about the assignment.
However, you should write y
Conditional distributions and conditional expectations
Discrete case
Suppose that X and Y are discrete random variables with joint mass function p(x, y). If y is a
real number with pY (y) > 0, then for any real number x,
P(X = x|Y = y) =
p(x, y)
P(X = x,
6
Jointly continuous random variables
Again, we deviate from the order in the book for this chapter, so the subsections in this chapter do not correspond to those in the text.
6.1
Joint density functions
Recall that X is continuous if there is a function
STAT 302 Midterm
Name
Student id
Important information about the midterm
Write your student number on each page.
The exam is closed book and has 5 questions.
Clearly dene any events and random variables. Ambiguous notations
might lead to mark deduction