Econometrics

[...]... kurtosis and presents the kurtosis as K-3 which means that a standard normal distribution receives a kurtosis of 0 Download free ebooks at bookboon.com 21 Econometrics Basics of probability distribution in econometrics 2 Basic probability distributions in econometrics In the previous chapter we study the basics of probability distributions and how to use them when calculating probabilities There exist a... determine the corresponding CDF: c P( X d c) f ( X )dX f Download free ebooks at bookboon.com 22 Econometrics Basics of probability distribution in econometrics Unfortunately this integral has no closed form solution and need to be solved numerically For that reason most basic textbooks in statistics and econometrics has statistical tables in their appendix giving the probability values for different... is, we have 8 ê X  4 E >Z @ E ô ằ ơ 8 ẳ êX 4 Eô ằ  ơ8ẳ 8 ê X  4 êX V >Z @ V ô ằ Vô 8 ằ ơ 8 ẳ ơ ẳ 1 4 E>X @  8 8 0, 1 V >X @ 1 64 Download free ebooks at bookboon.com 23 Econometrics Basics of probability distribution in econometrics Since any normally distributed random variable can be transformed into a standard normal random variable we do not need an infinite number of tables for all combinations... LEFT IRAN FOR A MASTERS IN PRODUCT AND PROCESS DEVELOPMENT AND LOTS OF INNEBANDY HELL TELL YOU ALL ABOUT IT AND ANSWER YOUR QUESTIONS AT MDUSTUDENT.COM www.mdh.se Download free ebooks at bookboon.com 13 Econometrics Basics of probability and statistics 1.1.4 The probability function the continuous case When the random variable is continuous it is no longer interesting to measure the probability of a... t a ) 1  F ( a) 3) P( a d X d b) F (b)  F (a ) In order to evaluate this kind of problems we typically use standard tables, which are located in the appendix Download free ebooks at bookboon.com 14 Econometrics Basics of probability and statistics 1.2 The multivariate probability distribution function Until now we have been looking at univariate probability distribution functions, that is, probability... in the joint probability function The marginal probability functions for X and Y is f (X ) Ư f ( X , Y ) for all X (1.6) y f (Y ) Ư f ( X , Y ) for all Y (1.7) x Download free ebooks at bookboon.com 15 Econometrics Basics of probability and statistics Example 1.12 Find the marginal probability functions for the random variables X P( X P( X P( X 1 2 1 4 1   16 16 16 16 4 2 4 2 8 1 1) f ( X 1, Y 0) ... 3 partial-tuition revolving scholarships worth 10,000! www.nyenrode.nl/msc *Keuzegids Higher Education Masters 2012, in the category of business administration Download free ebooks at bookboon.com 16 Econometrics Basics of probability and statistics 1.3 Characteristics of probability distributions Even though the probability function for a random variable is informative and gives you all information... formula we receive: 2 4 2 1 2 1  0 u 1u  0 u 2 u  1u 0 u  1 u 1 u  1 u 2 u  16 16 16 16 16 16 1 2 1 1 2 u 0 u  2 u 1u  2 u 2 u 16 16 16 E >X , Y @ 0 u 0 u Download free ebooks at bookboon.com 17 Econometrics Basics of probability and statistics 1.3.2 Measures of dispersion It is sometimes very important to know how much the random variable deviates from the expected value on average in the population... If they tend to vary in opposite direction, that is, when one tends to be above the expected value when the other is below its expected value, we have a negative Download free ebooks at bookboon.com 18 Econometrics Basics of probability and statistics covariance If the covariance equals zero we say that there is no linear relationship between the two random variables Important properties of the covariance... such as case competitions, sports, etc make new friends am ong cbs 18,000 students from more than 80 countries See what we look like and how we work on cbs.dk Download free ebooks at bookboon.com 19 Econometrics Basics of probability and statistics Example 1.16 Calculate the covariance and correlation for X and Y using the information from the joint probability mass function given in Table 1.7 Table . measurement that has more than one outcome and for which there is uncertainty about the result of the experiment. That is, the outcome of the experiment can not be predicted with certainty. Picking. following 8 outcomes represent the sample space for this experiment: (HHH), (HHT), (HTH), (HTT), (THH), (THT), (TTH), (TTT). Observe that each sample point is equally likely to occure, so that the probability. and their probability distribution. 1.3.1 Measures of central tendency There are several statistics that measure the central tendency of a distribution, but the single most important one is the