UKEQ 1013 QUANTITATIVE TECHNIQUES I ASSIGNMENT
Instruction:
1) It must be hand-written or type-written nicely.
2) Please provide cover page which includes all names of the group
members. One group consists of 6 to 7 members only.
3) The submission date is
Chapter 6
Discrete Probability Distributions
Organizing it into a frequency distribution
Portraying the distribution in tables, graphs,
and charts
Arithmetic mean, median, or mode
Range and the standard deviation
Probability (chap 5)
instead of desc
.
Just Take it Light
.
Sets
Definition. A Set is any well defined collection of
objects.
Definition. The elements of a set are the objects
in a set.
Notation. Usually we denote sets with uppercase letters, elements with lower-case letters.
The followi
Chapter 7
Continuous Probability
Distributions
Uniform Distribution
Normal Distribution
Uniform Distribution
The time to fly via a commercial
airliner from Florida to Georgia ranges
from 60 minutes to 120 minutes.
The time to prepare form 1040-EZ
follow
ST202 Probability Distribution Theory and
Inference
Week 5: Exercises
1. Find the maximum likelihood estimator for from a random sample from the
population with density function
f (yi ; ) =
2yi
0 < yi , > 0.
2
Do not use calculus. Draw a picture of the li
Problem Set 4 - Due on Monday Oct 24th
Ex. 1 Find (without generating functions) the mean and the variance for the following
distributions:
e kx xr 1 k r /(r 1)! x 0
(a) fX (x) =
r positive integer, k > 0
0
x<0
(A Gamma Distribution, Gamma(r,k)
x
(b) fX
ST202 - Michaelmas term
Probability and Distribution Theory
Kostas Kalogeropoulos
Conditional Probability and Independence
Random Variables
1 / 32
Introduction
Conditional Probability and Independence
Random Variables
Outline
1
Introduction
2
Conditional
Problem Set 8 - Due on Monday Nov 28
Ex. 1 Let
Y =
PN
i=1
Xi
0
if N 1
if N = 0
where cfw_Xi , i = 1, 2, . . . is a sequence of iid random variables and N is a discrete random
variable taking values 0, 1, . . . independent of cfw_Xi . Let KY (t) = log(MY
Solutions to Problem Set 7
Sol. Ex. 1
We know that R Pois( ) and we model K as a sum of R independent random variables
distributed as Bernoulli with probability of success (egg hatches) p. Then K|R = r
Bin(r, p). Since K|R = r has a binomial distribution
Problem Set 6 - Due on Monday Nov 14th
Ex. 1 (From the 2011 exam paper.) Consider the function
8
< k(x2 + y 2 ) if 0 < x < y < 1,
fX,Y (x, y) =
:
0
otherwise.
a. Under which conditions is fX,Y (x, y) the joint probability density function of X
and Y ?
b.
Problem Set 1 - Optional submission by Monday Oct 3
Ex. 1 An urn contains five balls numbered 1 to 5. We extract two balls with replacement.
a) Draw a diagram to represent the sample space for this experiment. Mark the following events on your diagram:
(a
Gamma distribution and exercise 2 problem set 7
The Gamma distribution has density
r
f (y) =
where
(r)
yr 1e
y
,
and r are positive and where
(r) =
Z
1
yr 1e
y
dy.
0
Check that f is indeed a density.
(
Note that its moment generating function is given by
Problem Set 3 - Due on Monday Oct 17
Ex. 1 Let G be the event that an accused is guilty, and T the event that some testimony is
true. Some lawyers have argued on the assumption P (G|T ) = P (T |G). When does this
hold?
Ex. 2 There are n urns of which the
Problem Set 2 - Due on Monday Oct 10
Ex. 1 A regular insurance claimant is trying to hide 3 fraudulent claims among 7 genuine
claims. The claimant knows that the insurance company processes claims in batches of 5
or in batches of 10. For batches of 5, the
me LONDON SCHOOL
or ECONOMICS AND
POLITICAL SCIENCE I
Summer 2015 examination
ST226
Actuarial Investigations: Financial
Suitable for all candidates
Instructions to candidates
This paper contains 9 questions. Answer All questions.
Time Allowed - Reading Ti
ST201/203
Statistical Models and Data
Analysis
Week 5
Sara Geneletti
Group exercise
List the goodness of fit statistics and their criteria and the
residual plots and what they are assumption they are
checking
SPSS
In this weeks workshop we will use both
ST201/203
Statistical Models and Data
Analysis
Week 8
Sara Geneletti
Introduction to Logistic Regression
We use logistic regression to model binary response
variables
i.e. (0,1) variables
Examples:
gender (male, female)
AIDS test (positive, negative)
ST201/203
Statistical Models and Data
Analysis
Week 10
Sara Geneletti
Recap from Week 9
Last week we learnt how to use moving averages to
deal with autocorrelation in time-series
We used them to de-seasonalise the time-series
Then we fitted a linear mo
ST201/203
Statistical Models and Data
Analysis
Week 7
Sara Geneletti
Modelling Strategies
So far we have looked at the main effects of
explanatory variables on the response variable
Today we are going to look at strategies to model
more nuanced effects
ST201/203
Statistical Models and Data
Analysis
Week 9
Sara Geneletti
Introduction
Time-series is any sequence of measurements of a
response variable over time
oil price across years
GDP of a country in quarters
or monthly sales of a company
They are
ST201/203
Statistical Models and Data
Analysis
Week 1: Introduction and Review
of Statistical Concepts
Sara Geneletti
Expectations
This course is aimed at students who have completed
ST107
If you have done ST102 and/or you are from
Accounting and Financ
ST201/203
Statistical Models and Data
Analysis
Week 2
Sara Geneletti
Announcements & Reminders
Make sure you have enroled on the moodle page
ST201/203
I am not going to be involved with the registers of the
workshop; ask your class teacher if you have i
ST201/203
Statistical Models and Data
Analysis
Week 6
Sara Geneletti
Model Selection
In Week 4 we learnt that the best model is that which
maximises its capacity to explain the response variable without
compromising its simplicity
Last week we learnt th
ST201/203
Statistical Models and Data
Analysis
Week 4
Sara Geneletti
Motivation for Multiple Linear Regression
Last week we saw simple linear regression, a linear
model where we only include one explanatory variable
The great advantage of multiple linea
ST201/203
Statistical Models and Data
Analysis
Week 3
Sara Geneletti
Recap of Week 2
Last week:
Elements of a model
Functional forms
Modelling process
Today:
Simple Linear Regression
Least squares estimation
Interpretation using Excel
Goodness of fit
2015/16 ST226 REVISION PROBLEMS 2
Please note that there might not be written answers to these problems, so you should attend the
lecture when they are discussed.
1. Two football clubs are trying to sign the same player. If club A signs the player its sha
2015/16 ST226 REVISION PROBLEMS 1 SOLUTIONS
1. Which one of
(p)
anj and anj
is larger? Explain your answer without the use of any equations.
(p)
anj Payment are made earlier.
2. Look up in your notes the interpretation of
1 = ianj + v n
and provide a simi
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