First Step
Analysis of
Markov Chain
Chapter 3.4 of textbook
1
Simple First Step Analysis
The Markov Chain cfw_Xn with state
space cfw_0,1,2 has the Markov matrix:
1
P
0
0
0
0
1
2
Questions
Let the time of absorption be
T minn 0 | X n 0 or X n 2
Find
u
Assignment 4
Requirements:
(1) Calculate the following ratios for the year of 2014 cfw_with formula and workings):
Liquidity and solvency ratios:
- Working capital
~ Current ratio
- Quick ratio
n Accounts receivable turnover
Number of days sales in recei
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CHAPTER 5 Accounting for Merchandising Businesses
Ex. 51
a. $931,000 ($2,450,000 $1,519,000)
b. 38% ($931,000 $2,450,000)
c. No. If operating expenses are less than gross profit, there will be a net
income. On the other hand, if operating expenses exceed
Ex. 523
3. FOLDAWAY FURNISHINGS COMPANY
Statement of Comprehensive Income
For the Year Ended February 28, 2014
Revenue from sales:
Sales
Less: Sales returns and allow.
Sales discounts
Net sales
Cost of Goods Sold
Gross profit
Expenses:
Selling exp
Ex. 3-10
a. Accounts Receivable 8,450
Fees Earned 8,450
Accrued fees.
b. No. If the cash basis of accounting is used, revenues are recognized only
when the cash is received. Therefore, earned but unbilled revenues would not
be recognized in the accounts,
Ch4 Completing the Accounting Cycle
P.207
EX 4-1 Flow of accounts into financial statements
The balances for the accounts listed below appear in the Adjusted Trial Balance
columns of the end-of-period spreadsheet. Indicate whether each account would
flow
Ex. 111
1st Year 2nd Year 3rd Year 4th Year
a. Total dividend declared . $24,000 $81,000 $92,000 $139,000
Preference dividend (current) . $24,000 $51,000 * $54,000 $ 54,000
Preference dividend in arrears . 301000 3:000
b. Total preference dividends . $
Ch11 Corporations: Organization, Share Transactions, and Dividends
Exercise 8 (Set 1 out of 2)
P.573
EX11-1 Dividends per share
Wallace Inc., a developer of radiology equipment, has share outstanding as follows:
30,000 shares of $90 par cumulative prefere
Week 2
Week
General definition of
Stochastic process, brief
introduction to
Martingales
and Branching processes
Stochastic Processes
A stochastic Processes is a family
of random variables X(t), or Xt,
where t belongs to an index set T.
Elements of a sto
Markov Chain
Chapter 3 in the text
book
1
Markov chain: Definition
A Markov process cfw_Xt is a stochastic process
with the property that, givn the value Xt, the
value of Xs for s>t are not influenced by the
value of Xu for u<t. A discrete-time Markov ch
Week 5
Long Run Behavior of
Markov Chains
Chapter IV of text book
1
Some Pn are convergent
It is not hard to verify that (using mathematical
induction) for a transition matrix
1 a
P
b
a
where
1b
0 a,b 1
we have
P
n
b
1
ab b
Note
lim
n
that
P
n
a
a
1
ab
a
The Classification of
States
Chapter IV, Section 3 of the
text book
1
Examples of irregular Markov
Example 1: identity matrix
1 0
1 0
n
P
P 0 1
0 1
Limiting probability exists but depends on initial state
Example 2:
0 1
1 0 2 n 1 0 1
2n
P
P 0 1 , P
1
Poisson Distribution and the
Poisson Process
Chapter V of text book
1
Poisson Distribution
The Poisson distribution with parameter > 0 is
given by
e
Pr X k p k
k!
k
Let X be a Poisson r.v. Then, E[X]= .
Moreover, E[X2] = 2+ and
Var(X) = .
Note: Poisson
Distributions associated with
the Poisson Process
Chapter V, Section 3 of the text book
1
Definitions
Wn: the waiting time of occurrence of
the n-th event. We often set that W0
= 0.
Sn: the sojourn time measures the
duration that the Poisson process
soj
Spatial Poisson Processes
Chapter V, Section 5 of the text book
1
Notations
Let S be a set of n-dimensional space
and A be a family of subsets of S.
A point process in S is a stochastic
process N(A) indexed by the sets A in
A and having the set of nonne
Spatial Poisson Processes
Chapter V, Section 5 of the text book
1
Notations
Let S be a set of n-dimensional space
and A be a family of subsets of S.
A point process in S is a stochastic
process N(A) indexed by the sets A in
A and having the set of nonne
4.3 Birth and Death Process
An obvious generalization of the pure
birth and the pure death process
discussed in Section 4.1 and 4.2 is to
permit X(t) both to increase and to
decrease. Thus it at time t the process is
in state n it may, after a random sojo
Renewal Phenomena
Chapter 5
1
5.1 Definition of a renewal Process
and Related Concepts
Renewal theory began with the study of
stochastic systems whose evolution through time
was interspersed with renewals or regeneration
times when, in a statistical sense
a.
b.
c.
Corrected financial statements appear as follows:
WE-SELL REALTY
Satement of Comprehensive Income
For the Month Ended August 31, 2014
Sales commissions
Expenses:
Office salaries expense
Rent expense
Automobile expense
Supplies expense
Miscellaneo
Introduction to
Introduction
Stochastic processes
Week 1: Review on basic tools
What is probability?
Probability is a concept trying to quantify
the likelihood for events which are not
certain to happen.
Probability cannot be simply described by
a sente