Problem Set 4. Independence
1. Consider a standard 6-sided die and a biased die with sides (1,2,3,4,6,6), i.e. one which has no
5 and two 6s. Assume you pick one of the two dice, with equal probabilit
Problem Set 4. Independence
1. Consider a standard 6-sided die and a biased die with sides (1,2,3,4,6,6), i.e. one which has no
5 and two 6s. Assume you pick one of the two dice, with equal probabilit
Problem Set 2. Counting
1. Fred is planning to go out to dinner each night of a certain week, Monday through Friday, with each
dinner being at one of his favorite ten restaurants.
i How many possibili
Problem Set 3. Conditional Probability
Instructor: Prof. Sotirios Damouras
Teaching Assistant: Mohsen Soltanifar
September 17, 2016
1. Suppose we deal five cards from an ordinary 52-card deck.
i What
Problem Set 5. Random Variables
1. Suppose that we roll two fair six-sided dice, and let Y be the sum of the two numbers showing.
Compute P (Y = y) for every real number y.
Solution: Define sample spa
STAB52 Quiz 1
Name:
Student Number:
Tutorial Number:
1. How many ways are there to permute the letters in the word T EN N ESSEE?
[3 marks]
2. A certain family have 8 children, consisting of 4 boys and
STAB52H3 Quiz 1
_
first
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last
student number
1. How many ways are there to permute the word NONNEGATIVE? [3]
2. There are n people in a room. Assume each persons birthday is equally likely to be any
STAB52 - Introduction to Probability Quiz 2 (week 5)
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Please show all your work! Answers without supporting work will not be
given credit. Write answers in
STAB52 Quiz 2
Please show all your work! Answers without supporting work will not be given
credit. Write answers in spaces provided. You have 50 minutes to complete this
quiz.
Full Name:
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STAB52 Week 7 quiz
Last Name: _
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Student Number: _
You have 50 minutes to complete this exam. Please note that no aids are allowed.
1. For X ~ Geom(p), find E(2x) given that it is finite.
STAB52 WEEK 5 QUIZ
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Score:
/20
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answers in spaces provided. You have 50 minutes to complete th
STAB52 Week 7 Quiz
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in spaces provided. You
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STAB52 WEEK 5 QUIZ
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Mark: _ /20
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answers in spaces prov
STAB52 WEEK 7 QUIZ
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UTSC
STAB52H3
MIDTERM EXAM
STUDY GUIDE
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STAB52H3 Week 5 Quiz _ _ _ _
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score /10
Please show all your work! Answers without supporting work will not be given credit. Write
answers in spaces provided. You have 50 minu
9. Expectation
STAB52 F17
Sotirios Damouras
STAB52 F17
1
Expected Value
RV X measures some aspect of a random experiment
Distribution of X defines uncertainty around X
Often, want to describe aggre
STAB52 F16 - LEC02
Quiz 8
Name (f,l):
ID #:
1. Consider rolling two standard fair dice, and let RVs X1 , X2 represent the result of each
die. Define the RVs Z = X1 + X2 and W = |X1 X2 |. Find the cond
STAB52 F16 - LEC02
Quiz 9
Name (f,l):
ID #:
1. Assume you roll 5 fair 6-sided dice; Find the probability that:
i. The minimum roll is equal to 1.
ii. The minimum roll is equal to 3.
Solution: Let X1 ,
STAB52 F16 - LEC02
Quiz 10
Name (f,l):
ID #:
1. Let the MGF of the RV X be mX (t) = eat , t R and some a R.
i. Find the mean of X.
ii. Find the variance of X.
iii. Show that X is a constant RV with va
UNIVERSITY OF TORONTO SCARBOROUGH
Department of Computer and Mathematical Sciences
STAB52H3 Introduction to Probability Summer 2017
Course Description: STAB52 is a mathematical treatment of probabilit
UNIVERSITY OF TORONTO SCARBOROUGH
Department of Computer and Mathematical Sciences
Midterm Test, June 2017
STAB52 Introduction to Probability
Duration: One hour and fifty minutes
Last Name:
First Name
CSC A67/MAT A67 - Discrete Mathematics, Fall 2017
Assignment #1: Proofs
Due: October 29, 2017 at 11:59 p.m. This assignment is worth 10% of your final grade.
Warning: Your electronic submission on Mar
6. Discrete Distributions
STAB52 F17
Sotirios Damouras
STAB52 F17
1
Discrete Distributions
Distribution of discrete RV Xcfw_x1,x2, is determined by
collection of all probabilities of the form
P( X= x
7. Continuous
Distributions
STAB52 F17
Sotirios Damouras
STAB52 F17
1
Continuous RVs
A RV X is called continuous if P(X=x)=0, x (i.e. PMF=0)
But can P(S)=1, when P(X=x)=0 , x?
YES, if X takes on un
8. Important Distributions
STAB52 F17
Sotirios Damouras
STAB52 F17
1
Distributions
Look at some additional common distributions:
Discrete
Negative Binomial
Poisson
Continuous
Gamma
Normal
STAB52
STAB52 - Introduction to Probability Quiz 4 (week 9)
Last Name:
Student #:
First Name:
Tutorial #:
Please show all your work! Answers without supporting work will not be
given credit. Write answers in
STAB52 Quiz 5
Please show all your work! Answers without supporting work will not be given credit. Write
answers in spaces provided. You have 50 minutes to complete this quiz.
Full Name:
Student Numbe
STAB52H3 Midterm Test
Sample Test
Duration: one hour and fifty minutes
Please do NOT open this booklet until you are asked to do so
There are 7 pages including this page. Please check to see if you ha
STAB52H Midterm Test
Saturday, June 9, 2007
Duration: one hour and fifty minutes
There are 8 pages including this page. Please check to see if you have all the pages.
Aids allowed: This test is open b