Two kind of strategies:
Mixed Strategies and Mixed Strategy Equilibrium
Two kinds of equilibrium
pure strategy mixed strategy
Two games with mixed strategy equilibria:
Matching Pennies Market Niche
Le modle IS-LM
Nous venons de voir avec le modle keynsien simple limportance de la manipulation de la demande dans une reprsentation agrge de lconomie, centre sur le
march des biens . Mais remarq
October 16, 2015
1. To encourage Elmers promising tennis career, his father oers him a prize if he wins (at
least) two tennis sets in a row in a three-set series to be played with his father and the club
champion alternately: fathe
M2S1 - EXERCISES 8
1. Suppose that X1 , ., Xn are a random sample from a P oisson() distribution. Define statistics
T1 = X =
T2 = S 2 =
(Xi X)2 .
Show, using properties of Poisson random variables and genera
Int. J. Contemp. Math. Sciences, Vol. 7, 2012, no. 24, 1205 - 1212
The Sampling Distribution of the Maximum Likelihood
Estimators from Type I Generalized Logistic Distribution
Based On Lower Record Values
Essam A. Amin
Department of Mathematics and Statis
Point Estimation of Parameters
and Sampling Distributions
Sampling Distributions and the central
Methods of point estimation
Sampling Distributions and the
central limit theorem
Chapter 8 Estimation of Parameters
and Fitting of Probability Distributions
8.5 The Method of Maximum Likelihood
Point Estimation: Let a random variable X have a pdf that is of known functional form, but depends on an unknown parameter . We assume that ma
2.7 Maximum likelihood and the Poisson distribution
Our assumption here is that we have N independent trials, and the result of each is n i
events (counts, say, in a particle detector). We also assume that each trial has the same
population mean , but the
Practice problems for Homework 11 - Point Estimation
1. (10 marks) Suppose we want to select a random sample of size 5 from the current CS 3341
students. Which of the following strategies is the best:
a) Pick 5 students from the rst row.
b) Pick 5 of your
Problem Set 5 and Exam Information
The exam is in class on Thursday, March 15th.
You are allowed to bring in two sheets of notes.
You will be given a handout that summarizes pdfs, their means, and their variances.
You are allowed to bring a calculator
Statistics 2 Lectures
Law of Large Numbers
Theorem (Law of Large Numbers). Let X1 , X2 , . . . be a sequence of independent random
variables with E(Xi ) = and var(Xi ) = 2 . Let Xn = n1 i=1 Xi . Then, for any > 0,
P(|Xn | > ) 0
In creating a parameter estimator, a fundamental question is whether or not the estimator differs from the parameter
in a systematic manner. Lets examine this by looking a the computation of the mean and the
Estimation in the continuous case, 3.5 and
October 2, 2012
Estimation in the continuous case, 3.5 and sampling distributions
The likelihood function
Recall the likelihood function is dened by,
Statistical Inference: Maximum Likelihood Estimation
Overview: Maximum Likelihood vs. Bayesian Estimation
Introduction to Maximum Likelihood Estimation
What is Likelihood and the MLE? . . . . . . . . . .
REPUBLIQUE DE COTE DIVOIRE
MINISTERE DETAT, MINISTERE DU
PLAN ET DU DEVELOPPEMENT
ECOLE NATIONALE SUPERIEURE DE
MINISTERE AUPRES DU PREMIER MINISTRE,
CHARGE DE LECONOMIE ET DES FINANCES
DIRECTION GENERALE DU TRESOR ET
PSTAT 120B Probability and Statistics - week5
University of California, Santa Barbara
November 2, 2012
PSTAT 120B Probability and Statistics
Topics for review
Hint for #1(9.69)
Hint for #2(9.80)
Hint for #3
PSTAT 120B Prob
Statistics - Lecture One
1. Basic ideas about estimation
2. Method of Moments
3. Maximum Likelihood
4. Condence Intervals
5. Introduction to the Bootstrap
Sampling Distributions & Point
What is a sampling distribution?
What is the standard error?
What is the principle of maximum
What is bias (in the statistical sense)?
What is a confidence interval?
What is the central
Ave Maria University
There are 6 parts to this exam, in 11 pages.
Attempt to answer all questions. Partial credit will be given.
o Unanswered questions will not receive any credit.
Winter Term 2004
Midterm #2 -Answers
Page 1 of 9
Midterm Exam No. 2 - Answers
April 1, 2004
Answer all questions, on these sheets in the spaces provided (use the blank space on page
8 if you need more). In questions where it is
Exam #2 Review Questions (Answers)
Exam #2 will cover all the material we have covered since Exam #1. This includes the
material we covered in Chapters 10, 11, 12, and 14. In addition to working these problems,
I would recommend reviewing all of
Some Answers for Chapter 7 homework
Problem 7.2 In mixed strategy equilibrium, the probability that the batter
prepares for a fastball is 6/7 and the probability that the pitcher throws a
fastball is 4/7.
Problem 7.4 x 4
Problem 7.5 This one is kind of a
KEEP 'EM GUESSING RANDOMIZED STRATEGlES
strategies assigned positive probability must yield the highest expected payoff,
and it is for that reason that a player is content to let a random device determine
how she behaves. If that weren't the case, the
Mixed-strategy Nash Equilibria
Leges sine moribus vanae
This chapter presents a variety of games with mixed-strategy Nash equilibria, many in the form of problems to be solved by the reader. Some
mixed-strategy equilibria, such as throwing ngers
Les formules mathmatiques composes avec L TEX sont de trois types :
des formules crites dans une ligne de texte
Montrez que, pour tout a > 0, on a limh0 a+h a = 2a .
des formules centres non numrotes :
Comment crire des formules avec
Version 2.0.2 du 06.1
Ralis avec : OOo 2.0.4
Plate-forme / Os : Toutes
Distribu par le projet fr
2 Insrer une formule dans un document.3
Proving that a Cobb-Douglas function is concave
if the sum of exponents is no bigger than 1
Ted Bergstrom, Econ 210A, UCSB
If you tried this problem in your homework, you learned from painful experience that the Hessian conditions for concavity of the Cob
Mixed Strategy Nash Equilibrium
In the Matching Pennies Game, one can try to outwit the
other player by guessing which strategy the other player
is more likely to choose.
However, by choosing the mixed strategy ( 1 1 ),
Approximation d'une loi binomiale par une loi normale.
Lorsque le paramtre n est grand, et que p est ni trop proche de 0, ni trop proche de l, on peut approcher la loi binomiale de
paramtres n et p par la loi normale de paramtres np et -Jnp( l-p).