Economic Statistics ECN 521
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This 3 page Class Notes was uploaded by Hannah Hahn on Wednesday October 21, 2015. The Class Notes belongs to ECN 521 at Syracuse University taught by Staff in Fall. Since its upload, it has received 40 views. For similar materials see /class/225648/ecn-521-syracuse-university in Economcs at Syracuse University.
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Date Created: 10/21/15
ECONOMIC STATISTICS Economics 521 Probability Theory Experiment Outcome Sample Space S Set of all possible outcomes Event Subset E of the Sample Space S Probability Function A mction P from events to the real numbers such that 1 PE 2 0 2 PS 1 3 A m B 21 implies PA u B PA PB A Complement ofA A u A S andA m A 3 So PA PA PA u A PS 1 PA 1 PA H a PA PA PA g 1 mg 0 IfE1 E2 21 and E2 m E 21 and E1 m E Q then 1 03 U E2 U E PEl PEz PEg If E E2 EL are pairwise disjoint then PE1 u E2 u u E PEl PEz PE a PA u B PA PB PA m B STAT02 1 Elementary Events Equiprobable elementary events PA A S It Fundamental Counting Rule 1 Suppose a process can be carried out in two stages the rst stage can be carried out in m ways while the second stage can be carried out in n ways Then the whole process can be carried out in m X n ways 2 Suppose a process can be carried out in three stages the rst stage can be carried out in m ways while the second stage can be carried out in n ways and the third stage can be carried out in r ways Then the whole process can be carried out inm X n X r ways Examgles 1 Number of outcomes of 10 successive coin ips P Number of ve letter quotwordsquot LN Number of possible six entry alphanumeric license plates 4 With ordinary poker deck the number of ve card dealings 311875200 U The number of permutations of n things taken r at a time 0 With ordinary poker deck i The number of two card hands ii The number of three card hands iii The number of ve card hands 2598960 The number of combinations of n things taken r at a time STAT02 2 Poker deck 52 cards distinguished by color suit and denomination 26 Red Suits are hearts 13 and diamonds 13 26 Black Suits are spades 13 and clubs 13 13 denominations Within each suit 2 3 4 5 6 7 8 9 10 Jack J Queen Q King K Ace A Poker hands Royal ush 10JQKA in one suit Straight ush sequential denominations in one suit Four of a kind Full house Three of one denomination two of another Flush one suit Straight sequential denominations Three of a kind Two pair One pair Not even one pair or better STAT02 3
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