Solution of Assignment 1
1. (a) Let event E denote that 1 appears before 6 in the sequence. Conditioning on
the outcome of the rst toss, we have:
6
P (E |1st = i)P (1st = i)
P (E ) =
i=1
=
14
+ P (E )
Stat 333
Spring 2009
Assignment #1
The assignment is due Tuesday, May 26 in class. It will be posted in segments, and I will let you know when all segments have been posted and the assignment is compl
Assignment #1 (Due on Oct. 11th in the class)
1. Suppose we toss a fair die repeatedly and independently. We get a sequence of numbers.
(a) Find the probability that 1 appears before 6 in the sequence
Stat 333 - Assignment 1 Solutions - Fall 2011
1.
(a) We will dene random variables Ij to indicate the state of computer j , j = 1, 2, 3, 4.
Therefore,
Ij =
, if computer j is isolated
, if computer j
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: 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
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 - Spring 2014 - Assignment 2 SOLUTIONS
1. Suppose we toss a fair coin repeatedly and observe a sequence of H or T. Let be the event
T T H H.
(a) Why is a renewal event?
Because it is a patter
Stat 333
Winter 2009
Assignment #3
The assignment is due Friday, April 3 , in class. Questions 14 posted March 14: These should be done before the term test 1. (a) Letters are drawn randomly with repl
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 Assignment 3 SOLUTIONS
1. At all times, a container holds a mixture of N balls, some white and the rest black. At each
step, a coin having probability p, 0 < p < 1, of landing heads is tossed
STAT 333 Assignment 1
Due: Thursday, May 29 at the beginning of class 1. Consider 10 independent coin flips having probability p of landing heads. We say a changeover occurs whenever an outcome differ
STAT 333 Assignment 1 SOLUTIONS
Due: Thursday, Sep. 30 at the beginning of the class
Chapter 1
1. (#18)Assume that each child who is born is equally likely to be a boy or a girl. If a
family has two c
STAT 333 Spring 2009 Solutions to Assignment 1
By Juan Manuel Martinez e-mail:[email protected] June 3, 2009
Type I Problems
Problem 1
a) Here T has an exponential distribution with parameter =
STAT 333 Assignment 1
Due: Thursday October 6 at the beginning of class
1. Suppose four computers are joined in a network according to the following diagram. (The
double lines indicate two separate co
STAT 333 Assignment 1 SOLUTIONS
1. Consider 10 independent coin flips having probability p of landing heads. a. Find the expected number of changeovers. Let Xi = 1 if there is a changeover between tri
STAT 333: Applied Probability
Homework 3
Instructions:
Due Monday, April 6 at 5pm in Drop Box 15, Slots 2 & 4.
Include the names of all collaborators.
1. An auto insurance company receives claims from
STAT 333: Assignment #3
(Due: July 30th before 3:00pm in my oce)
1. Consider the Markov chain with the state space S = cfw_0, 1, 2, 3, 4 and the transition matrix
0
0 1/5
1 0
P = 2 0
3 0
4 0
1
1/5
1/3
Question 1. (10pts)
Let X1, X2, X 3 . , . be independent and identically distributed random variables from Binomial distribution
with size 2 and probability 0.5. That is, for any n 2 1,
P(Xn : 0) z 0.
Stat 333
Winter 2009
Assign #1
Selected Partial Solutions
1. A is right and the guard is wrong. That is, if we let B = the guard says B is going free, then P (A executed) = P (A executed|B ) = 1/3. In
STAT 333 Assignment 1
Due: Thursday, May 27 at the beginning of class 1. Consider rolling a fair 6-sided die n times. Let X represent the number of faces that have NOT been rolled. a. Find the expecte
Answers for the review problems about the basic concepts of the
probability
Chapter 1
1. Let A and B be two events.
(a) Show that in general, if A and B are disjoint, then they are not necessarily ind
Solutions for Practice Questions in Chapter 4.
1. (a)
s
5 + 3s
1
s
5 1 + 3s/5
C (s) =
=
Using the alternative geometric series, we have
C (s) =
s
3
1
s
s
=
5 1 + 3s/5
5 n=0
5
n
=
1
3
5
5
n=0
n
sn+1 .
STAT 333 Assignment 2 SOLUTIONS
Due: Thursday, June 26 at the beginning of class 1. Suppose we toss a fair coin repeatedly and observe a sequence of H or T. Let be the event H H T T . a. Why is a rene
Chapter 7
Continuous markov process
In this chapter, we are still interested in the continuous process
cfw_X(t), t 0.
The following are some concepts related to the continuous process.
1. State space
STAT 333: Assignment 2
Due: Nov. 7th in class, or in Pengfei or Martins oce no later than 4pm on Nov. 8th.
Note: Please use the cover page for the assignment. No cover page=0%.
1. Let X1 , X2 , X3 , .
Assignment #2 (Due on Nov 13th in the class)
Note 1: Please use the cover page for this assignment.
Note 2: The pgf of Geo(p) rv is
ps
.
1(1p)s
You can directly use it without proof.
1. Suppose X NegB
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