Question 1. (8pts) Suppose that 8 cards, of which 4 are red cards and 4 are green cards, are put at
random into 8 envelope, of which 5 are red envelope and 3 are green envelope, so that each envelop w
STAT 333 Assignment 1 SOLUTIONS
1. Consider 10 beads on a bracelet having probability p of being blue and probability 1 - p of
being purple. We say a changeover occurs whenever a bead is a different c
University of Waterloo
STAT 333 Midterm
Term: Fall
Year:
2012
Student Name (Print):
UW Student ID Number:
UW Student Userid:
Instructor (Circle one):
1. Pengfei Li
2. Mehdi Molkaraie
Course Abbreviati
Stat 333 Homework 1
Instructions: Due Thursday, Oct 8 at 6:30pm in drop box # 14. Questions
1-6 are worth 5 points each.
1. Suppose that there are K types of butteries in a forest. A scientist goes to
STAT 333 Assignment 1
1. Two fair dice are thrown. Let X be the score on the rst die, and Y be the larger
of the two scores.
(a) Write down a table showing the joint distribution of X and Y .
(b) Find
STAT 333 - Spring 2014 - Assignment 1
Due Thursday June 5 at start of class
This assignment may be completed in pairs. Only one person should submit the paper. Both
names and ID numbers should be on i
STAT 333: Assignment #3
Due: Dec. 1st in Pengfeis oce no later than 4pm.
Note: Please use the cover page for the assignment. No cover page=0%.
1. Consider the Markov chain with the state space S = cfw
STAT 333
Midterm Solutions February 2008
AIDS: Calculator, Formula sheet
DURATION: 60 minutes
1. Each part is worth 2 marks
(a) Let I1 , . . . , In be independent indicator random variables (rvs) such
STAT 333: Applied Probability
Homework 1
Instructions:
Due Tuesday, October 18 at 5pm in Drop Box 15, Slots 1-3 for Section 1, Slots 4-6 for Section 2.
Include the names of all collaborators.
1. Prove
Stat 333 Homework 3
Instructions: Due Monday, Nov 30 at 6:30pm in drop box # 14. Questions
1-6 are worth 5 points each.
Print and attach this page as your cover page. Failure to do so will result in
a
Stat 333 Homework 1
Solution
K
j=1
1. Let Ij = 1 if buttery type j is caught, and Ij = 0 otherwise. Then X =
and
K
K
j=1 Ij
E[X] = E
=
E[Ij ] = KE[I1 ] = KP (I1 = 1),
j=1
where the second-last equalit
STAT 333 Assignment 2 SOLUTIONS
Due: Thursday, Nov. 4 at the beginning of the class
1. let Xi , i = 1, 2, .n, are i.i.d. random variables with uniform distributions on [0, 1], where
n is a positive in
1
Essentials of Stochastic Processes
Rick Durrett
Version Beta of the 2nd Edition
August 21, 2010
Copyright 2010, All rights reserved.
2
Contents
1 Markov Chains
1.1 Denitions and Examples . . . .
1.2
Chapter 2
Poisson Processes
2.1 Exponential Distribution
To prepare for our discussion of the Poisson process, we need to recall the
denition and some of the basic properties of the exponential distri
STAT 333: Assignment 1
Due: October 9th in class, or in Pengfei or Martins oce no later than 5pm on October 10th.
Note: Please use the cover page for the assignment.
1. A collection of n coins is ippe
Markov process with infinite number of states
(Q9 of Ch5 of the supplementary notes)
Suppose we have a revised random walk with a boundary at 0. That is, the walk takes
values only in the nonnegative
STAT333 Spring 2017 Tutorial #5
1. Consider a sequence of Bernoulli trials and P (S) = p with 0 < p < 1. Let =SF and T be
the waiting time for observing the first SF in the sequence. We say that the e
622:
(a) pro/9: PCTIaeéép) :PCRM 45) :{bE)I: 3%?)10
(b)
Add-WI:
mWQ W VWD% 2000 605 [W5
*mm o 4/: mm
Em VIt VWjIA Mae 9/ a.
MOI/W
{2) T I"; WWW 75) Walt >000
19% TW m c 220)
Pro I: b4 >000 M, 0 Is"
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Solutions for Practice Questions in Chapter 4.
1. (a)
C(s) =
=
s
5 + 3s
1
s
5 1 + 3s/5
Using the alternative geometric series, we have
C(s) =
s
3 n X
1
sX
1 3 n n+1
s =
=
s
.
5 1 + 3s/5
5 n=0
5
5
5
$7,717? 5 TWIM 3
a]: 0445,. v. .I
wire WW / mdA MBWMI mmrf nmg
m w
mwnm 5f, BM (my) 7 3m E M.
X;#4 5'! DA EN 13"
X3 HEN Bin (mm?)
w E(XY):EC CHEW) :Eag? .: MfWHWJLMImf
I/mrr) \ : nayrm 1% EM".
+[E
August 1, 2016
1
Competitive Equilibrium
Competitive Equilibrium (Assumptions): People live for only two periods, 0 and 1.
Competitive Equilibrium (Denition):
Given (t0 ; t1 ; y0 ; y1 ; r), the compet
Stat 333: Applied Probability
Winter 2018, University of Waterloo
Notes taken by Peter Liao
Id love to hear your feedback. Feel free to email me at [email protected]
See cthomson.ca/notes for upd
Stat 333 my Practice Collection
Question 1: A coin is continually tossed, where probability of H on a toss is 12 ,
find the following:
(a) P (1st two tosses give HH)
(b) P (1st two tosses give T H)
(c
CS 246 Spring 2017 - Tutorial 8
June 27, 2017
1
Summary
Class Relationships
Inheritance
Encapsulation and Inheritance
Polymorphism
Arrays and Inheritance
override and virtual
2
Class Relationshi
STAT333
Summary of Chapter 4
The purpose of this chapter is four-fold. First, given a sequence of real numbers cfw_an
n=0 ,
how to calculate the generating function A(s). Second, given the generating