Tutorial 5, Friday, 31 October
MA30125/MA50125
Page 1 of 4 pages
Solutions to Problems
Problem 1.
(a) Both Q-matrices are irreducible, and since the state space is finite, they have a unique stationary
distribution. To find these, we need to solve the sys
Tutorial 10, Friday, 5 December
MA30125/MA50125
Page 1 of 3 pages
Solutions to Problems
Problem 1.
We check that the Optional Stopping Theorem can be applied. We have |Mn | maxcfw_a, b =: C
whenever n S. So it remains to check that S < with probability 1.
Tutorial 8, Friday, 21 November
MA30125/MA50125
Page 1 of 4 pages
Solutions to Problems
Problem 1.
Recall the diagram:
n3
n
3
n4
n
4
I[n2 > 0]
I[n1 > 0]
q n
n
1
2
I[n2 > 0]
2I[n1 > 0]
2I[n2 > 0]
(a) We have
3 1
1 4
0
Q=
0
0
0
0
(b) We need
X
( 1 )
n1
n
Tutorial 4, Friday, 24 October
MA30125/MA50125
Page 1 of 3 pages
Solutions to Problems
Problem 1.
(a) Regardless of how many lines are in use, a new line is requested at rate . So we have qi,i+1 = ,
i = 0, 1, . . . , C 1. When there are i lines in use, th
Tutorial 1, Friday, 3 October
MA30125/MA50125
Page 1 of 3 pages
Solutions to Problems
Problem 1.
(a) The mean and variance of Xt are easily found from the mean and variance of the compound
Poisson process (see Section 1.7). We have
E[Xt ] = x0 + ct tE[Y1
Tutorial 6, Friday, 7 November
MA30125/MA50125
Page 1 of 3 pages
Solutions to Problems
Problem 1.
(a) Let
n1 = # of cars unused;
n2 = # of cars in use by a customer;
n3 = # of cars under repair.
The diagram of the closed migration process is the following
Tutorial 2, Friday, 10 October
MA30125/MA50125
Page 1 of 2 pages
Solutions to Problems
Problem 1.
(a) If the i cells are spread over a disc of area ci, then there will be approximately c i cells on the
boundary of the disc. Each of these cells
is assumed
Tutorial 3, Friday, 17 October
MA30125/MA50125
Page 1 of 3 pages
Solutions to Problems
Problem 1.
(a) From the diagramm we have:
2 1
Q = 4 4
2
1
1
0 .
3
(b) The eigenvalues of Q can be found by solving det(x Q) = 0. Computing the determinant and
simplifyi
Tutorial 7, Friday, 14 November
MA30125/MA50125
Page 1 of 3 pages
Solutions to Problems
Problem 1.
Recall the diagram:
1
n1
I[n1 > 0]
n3
n3
n3
2n3
I[n2 > 0]
2
n2
Recall also the invariant vector:
=
21 + 2 21 + 32 1 + 2
,
,
,1 .
Recall the form of the s
The Online Library of Liberty
A Project Of Liberty Fund, Inc.
Irving Fisher, The Purchasing Power of Money, its
Determination and Relation to Credit, Interest and
Crises [1911]
The Online Library Of Liberty
This E-Book (PDF format) is published by Liberty
ECON 3010
Intermediate Macroeconomics
Chapter 4
The Monetary System:
What It Is and How It Works
Money: Definition
Money is the stock
of assets that can be
readily used to make
transactions.
Money: Functions
medium of exchange
we use it to buy stuff
stor
TLT-5400/5406 DIGITAL TRANSMISSION, 1st Matlab-Exercise
In this exercise, we consider the generation of baseband PAM based digital communications waveforms with Nyquist
pulse-shaping. Also the effect of additive noise is demonstrated. So we study, e.g., h