Lecture Stat 302 Introduction to Probability - Slides 1
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Administrative details
Arnaud Doucet, O ce LSK 308c, Department of Statistics & O ce ICCS 189, Department of
Lecture Stat 302 Introduction to Probability - Slides 20
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Conditional Distributions: Discrete Case
Given a joint p.m.f. for two r.v. X , Y it is possible to comput
Lecture Stat 302 Introduction to Probability - Slides 21
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Conditional Distributions: Discrete Case
Given two r.v. X , Y , we have Discrete p (x , y ) p ( x ,y ) pX
Lecture Stat 302 Introduction to Probability - Slides 22
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Characterizing Joint Distributions/Densities: Covariance
Consider two r.v. X and Y (either discrete or co
Lecture Stat 302 Introduction to Probability - Slides 23
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Exercise 1
Alf and Beth are two UBC students. They must take 4 300-level courses from a list of 12 possib
If one can calculate the simple average of a data set, under what conditions and why weighted average
is calculated. Use some data to support your position.
A simple average of a data set is very usef
Discuss the importance of the Central Limit Theorem.
Search the Internet and find a website in which you can experiment with the Central Limit Theorem. Using the
website, illustrate at least three dif
Random Variable Distributions
Sunday, December 18, 2016
5:13 PM
Distribution
Description
Binomial
(Discrete)
Number of successes in a sequence of n independent Bernoulli trials, each with probability
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 repres
STAT302: Introduction to Probability
Fall 2014-15
Assignment 3
Due date: see course website (Under Schedule).
Instructions
Academic integrity policy: I encourage you to discuss verbally with other stu
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 stu
STAT302: Introduction to Probability
Fall 2014-15
Assignment 3
Due date: see course website (Under Schedule).
Instructions
Academic integrity policy: I encourage you to discuss verbally with other stu
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 stu
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 stu
Lecture Stat 302 Introduction to Probability - Slides 19
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Sum of Independent Random Variables
Consider Z = X + Y where X and Y are disrete r.v. of respective p.m.f
Lecture Stat 302 Introduction to Probability - Slides 18
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Jointly Distributed Random Variables
If both X and Y are continuous r.v., then their joint p.d.f. is a no
Lecture Stat 302 Introduction to Probability - Slides 17
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Jointly Distributed Random Variables
Assume we have two r.v. X and Y , then we dene the joint c.d.f. F (a
Lecture Stat 302 Introduction to Probability - Slides 2
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Recapitulation
Principle of counting: If experiment 1 has n1 possible outcomes, experiment 2 has n2 possible
Lecture Stat 302 Introduction to Probability - Slides 3
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Sample Space
Denition. The sample space S of an experiment (whose outcome is uncertain) is the set of all possi
Lecture Stat 302 Introduction to Probability - Slides 4
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Axioms of Probability
Consider an experiment with sample space S . For each event E , we assume that a numbe
Lecture Stat 302 Introduction to Probability - Slides 5
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Conditional Probabilities
Conditional Probability. Consider an experiment with sample space S . Let E and F
Lecture Stat 302 Introduction to Probability - Slides 6
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Independence
We say that the events fEi gn=1 are independent if i P (\n=1 Ei ) = i
i =1 n
P ( Ei ) .
and if
Lecture Stat 302 Introduction to Probability - Slides 7
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Simpson Paradox: Sex Bias in Graduate Admissions? s
The University of California at Berkeley was sued for bi
Lecture Stat 302 Introduction to Probability - Slides 8
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Expected Value
The expectation of X , denoted E (X ), is dened as E (X ) =
i =1
xi p (xi ) =
x p (x )
x :p
Lecture Stat 302 Introduction to Probability - Slides 9
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Example: Optimal Stock
Vancouver 2010 Olympic Torchbearer red mittens are currently sold at a net prot of b
Lecture Stat 302 Introduction to Probability - Slides 10
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Discrete Random Variables
A discrete r.v. X takes at most a countable number of possible values fx1 , x2 ,
Lecture Stat 302 Introduction to Probability - Slides 11
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Discrete Random Variables
A discrete r.v. X takes at most a countable number of possible values fx1 , x2
Lecture Stat 302 Introduction to Probability - Slides 12
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Hypergeometric Random Variable
Consider a barrel or urn containing N balls of which m are white and N m a