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Midterm
Studies in Economic Statistics
Spring 2004
J.Y. Kim
1. Let X be a random variable dened on a probability space (, F , P ). Show that X
induces a probability space (R, B , Q) by rst dening B and Q. (8pts)
2. Let (, F , P ) be a probability space. L
2015. 09. 11. ()
40 ?
Conventional Oil & Gas
Unconventional Oil & Gas
E&P
Q&A
Regional Primary Energy Consumption
Coal
Renewable
Hydro
Nuclear
Gas
Oil
BP Statistical Review of World Energy 2015
Note
Proved Oil Reserves
Reserves are those qu
Problem Set 4
1. Williamson, Chapter 10, Problem 7.
2. Williamson, Chapter 10, Problem 9.
3. Williamson, Chapter 11, Problem 9.
4. Suppose a rm produces only using capital, so output in any period is Y = zF (K).
Capital depreciates fully, so investment is
Midterm Exam
Spring 2009
J.Y.Kim
1. (a) Let An , n = 1, 2, . . . be a sequence of events such that limn An = A for an event
A. Prove that limn P [An ] = P [A] for a probability measure P .
(b) Write the Borel-Cantelli Lemma (1st version), and prove it.
2.
Midterm
Studies in Economic Statistics
Spring 2005
J.Y. Kim
1. Let X be a random variable dened on a probability space (, F , P ). Show that X induces
a probability space (R, B, Q) by rst dening B and Q. (8pts)
2. Let Xi i.i.d.(, 2 ) for i = 1, , n. Show
Midterm Exam
Spring 2008
J.Y.Kim
1. Let X be a random variable dened on (, F , P ). Let (R, B , PX ) be the induced
probability space and FX be the corresponding cumulative distribution function. Also,
let g : R R be a Borel measurable function. Dene the
Midterm Exam
Spring 2007
J.Y.Kim
1. Let F be a class in a space and let F1 , F2 , . . . be classes in a common space .
Determine whether each of the following statements is true of false and explain why.
(a) Suppose that F and that A, B F implies (A \ B )
Midterm
Spring 2006
J.Y.Kim
Solve the following problems.
1. Let = (0, 2]. Denote by I = (a, b] for 0 a, b 2. Also, denote by |I | = b a.
Let A be a set such that A = i Ii = i (ai , bi ]. Also, let P () be a function such that
P (A) = i |Ii |/2 for mutual
Abstract
Midterm
Studies in Economic Statistics
Spring 2003
J.Y. Kim
1. Let be the unit square cfw_(x, y ) : 0 < x, y 1, let F be the class of sets of the
form cfw_(x, y ) : x A, 0 < y 1, where A B , and let P (A) have value (A) where
denotes the Lebesqu
Chapter 2. Conditional Expectation and
Projection
Source: Bruce E. Hansens textbook
Studies in Econometrics
Autumn 2015
1 / 17
Wage Distributions
Probability distribution
Mean, median and quantiles
log transformation
2 / 17
Conditional Expectation
m(x) E(