WHAT IS CONSENT AND HOW CAN IT BE GRANTED?
Consent is a permission given to approve the actions of other persons. Giving my consent to
be governed by the decisions of the majority is one such example. In giving consent to
another persons proposal, we auth

Usually we have sample data
Therefore the model holds only in the range
of observed value
When predicting demand one should
therefore choose independent variables in
this range
The reason is that the model may not hold
outside the observed values
Manager

Philosophical Essays
Critical Thinking Lecture 4
Philosophical Method
Philosophy different in many ways from other
academic subjects
It has little if any empirical component
But this does not mean it lacks methodology.
Philosophy always proceeds by ar

Failures of Reason
Critical Thinking lecture 5
Fallacies and Rhetoric
Rhetorical Ploys are devices that appeal to
emotion, etc., but without employing
argument forms.
Fallacies are faulty forms of argument:
Formal fallacies (these are simply invalid)

Of course we use computer programs
Simple regression Y on P:
Standard error of estimate =16.4324
Model Summary
Model
1
R
.866a
R Square
.750
Adjusted
R Square
.719
Std. Error
of the
Estimate
16.4324
a. Predictors: (Constant), P
Managerial Economics
1
Lin

Think
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EVOLUTION AND THE MODERN DEUS EX
MACHINA
Margaret Betz
Think / Volume 11 / I

Essay Intros
What is the Paradox of the Stone?
Does it prove that God is not
omnipotent?
Omnipotence is described as being all-powerful: A being who is
omnipotent would be able to bring about any state of affairs and
have the power to perform any action t

Bertrand Russell On Induction (Ch. 6 of The Problems of Philosophy)
In this chapter, Russell argues that there is no rational justification deriving from experience for
drawing inductive inferences, and yet drawing such inferences is something that we can

Assignment 2: Business Forecasting
Provide copies of your answers by Wednesday, November 18, 2015. You will be contacted with the details on how, where and when to submit your answers. You can obtain
up to 5 marks counting towards the nal mark for this se

Arguments in Philosophy
Critical Thinking Lecture 3
Our Reading
Bertrand Russell, On Induction
Note that this is a chapter taken from The
Problems of Philosophy
So not every part of the argument is contained
in this chapter.
All the same, it is a usef

Each of these multiple-choice questions has exactly ONE correct
answer.
Complete this Assessment Online via Blackboard
1. Consider the following two linear equations in x and y :
4x+3y = 2
3x+2y5 = 0.
Which of the following statements is correct?
A. There

ECON10072 Advanced Statistics
Exercise Sheet 4
1. The continuous random variable X has probability density function given by
f (x) =
(
0:1 + kx; 0 x 5;
0; otherwise:
(a) Find the value of the constant, k; which ensures that this is a proper density functi

ECON10072 Advanced Statistics
Exercise Sheet 2
1. A and B are events such that Pr(A) = 0.4 and Pr(A B) = 0.75.
(a) Find Pr(B) if A and B are mutually exclusive.
(b) Find Pr(B) if A and B are independent.
2. Events A, B and C are such that B and C are mutu

ECON10072 Advanced Statistics
Exercise Sheet 1
Note: You are expected to attempt these questions prior to your tutorial and to bring your
solutions with you to the class.
Some of the questions below refer to the Excel le ExSheet1.xls. This can be found on

ECON10072 Advanced Statistics
Exercise Sheet 3
1. The discrete random variable Y has the following pmf :
y
-2
-1
0
1
2
p(y)
0.1
0.2
0.4
0.2
0.1
(a) Show that E[Y ] = 0.
(b) More generally, a discrete random variable Y is said to symmetric around zero if P

ECON10071
Exercise Class: Problem Sheet 1 - Extra
Logic & Functions
Notes on Solutions
These problems relate to the material and related readings for Lectures 0 and
1.
1. Let N be any positive integer: N 2 N:
(a) Show that 2N is even if N is even. (N even

ECON10071
Exercise Class: Problem Sheet 7
Unconstrained Bivariate Optimisation
These problems relate to the material and related readings for Lecture 12.
1. Show that the following functions are concave, where in both cases
> 0, x1 > 0 and x2 > 0
> 0;
(a)

ECON10071
Exercise Class: Problem Sheet 2 - Extra
Dierentiation, Stationary Points, Concavity/Convexity, Global/Local
maxima
Notes on Solutions
These problems relate to the material and related readings for Lectures 2-4.
1. Suppose that competitive rms pr

1
ECON10071
Exercise Class: Problem Sheet 3 - Extra
Dynamics and Linear Dierence Equations
These problems relate to the material and related readings for Lectures 5 and
6.
yt+1 yt
:
yt
Suppose the proportionate rate of growth of y is a constant r > 0; for

ECON10071
Exercise Class: Problem Sheet 5 - Extra
Matrices
1. For the matrix
A=
0:95 0:1
0:05 0:9
:
see if you can make any headway with following problem.
Let z = (z1 ; z2 )T ; be a (2 1) vector with at least one element non-zero (so that
z 6= 0), and 2

Exercise Class: Problem Sheet 6 - Extra
Bivariate Functions, Surfaces & Partial Derivatives
1. Let f (x1 ; x2 ) = x21 + 2x1 x2 + x22 :
(a) Find f ( 1; 2); f (z; z) and f (a + h; b)
f (a; b):
(b) Prove that f (2x1 ; 2x2 ) = 4f (x1 ; x2 ) and that f (tx1 ;

Implicit
Differentiation
Sometimes functions are given not in the form y = f (x) but in a more complicated form in which
it is difficult or impossible to express y explicitly in terms of x. Such functions are called implicit
functions. In this unit we exp

Integration
Mario Pezzino
ECON10071 ADVANCED MATHEMATICS
University of Manchester
Integration
Aims & Objectives
1. To introduce the formal Zdenition of the integral of
mathematical function, f (x )dx
2. Basic rules of integration
3. Substitution
4. Integr

ECON10071
Exercise Class: Problem Sheet 7 - Extra
Unconstrained Bivariate Optimisation
1. Show that the following functions are concave, where in both cases
> 0, x1 > 0 and x2 > 0
(a) f (x1 ; x2 ) =
ln (x1 ) +
(b) f (x1 ; x2 ) = x1 x2 ;
> 0;
ln (x2 )
+
1.

ECON10071
Exercise Class: Problem Sheet 1 - Extra
Logic & Functions
1. Let N be any positive integer: N 2 N:
(a) Show that 2N is even if N is even. (N even is su cient, but not
necessary, for 2N to be even.)
(b) Show that 3N is odd, if and only if N is od

ECON10071
Exercise Class: Problem Sheet 6
Bivariate Functions, Surfaces & Partial Derivatives
1. Let f (x1 ; x2 ) = x1 x22 : Find f (0; 1); f (2; 1); f (104 ; 10
2)
and f (z; z):
2. For each of the following functions
f (x1 ; x2 ) = x31
3x1 + x22
f (x1 ;

ECON10071
Exercise Class: Problem Sheet 7
Unconstrained Bivariate Optimisation
2 3
a (2 2) matrix. Dene
3 8
1) vector b = Ax = (b1 ; b2 )T and the quadratic form q = xT Ax:
1. Let x = (x1 ; x2 )T 2 R2 ; be a (2
the (2
1) vector, A =
(a) Write expressions

ECON10071
Exercise Class: Problem Sheet 2 - Extra
Dierentiation, Stationary Points, Concavity/Convexity, Global/Local
maxima
1. Suppose that competitive rms prot function can be written in the form
(q) = pq
c(q); q
0
where c(q) is the cost function and p

ECON10071
Exercise Class: Problem Sheet 8
Constrained Optimisation
The [*] questions will be given priority in the Exercise Class.
1. [*] Dene
f (x1 ; x2 ) = 2x1 + 3x2
and
g(x1 ; x2 ) = x21 + x22
20
(a) In the (x1 -x2 ) plane; draw the straight lines indi