Lecture_21_E7_L21_Statistics_F07-1

# Lecture_21_E7_L21_Statistics_F07-1 - 1 E7: INTRODUCTION TO...

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E7: INTRODUCTION TO COMPUTER E7: INTRODUCTION TO COMPUTER PROGRAMMING FOR SCIENTISTS AND PROGRAMMING FOR SCIENTISTS AND ENGINEERS ENGINEERS Lecture Outline Review of probability Discrete random variable and mass probability function Continuous random variable and probability density function (pdf) Normal pdf, mean and standard deviation E7 L21 1 Copyright 2007, Horowitz, Packard. This work is licensed under the Creative Commons Attribution-Share Alike License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/2.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

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E7 L21 2 Probability - review Probability - review Experiment : A situation whose outcome depends on chance Sample Space S:  set of all possible outcomes of an experiment Outcomes : elements of the sample space S Events : subsets of the sample space S Example: throwing of a dice once S = The event of observing an even number of dots: E =
Probability - review Probability - review Probability : A number between 0 and 1, inclusive, that indicates how likely an event is to occur . Probability of event A is denoted as P(A) . The closer P(A)   to 1 , the more likely is A   to happen. Frequentist approach to assigning probability : Repeat an experiment many times, under the same conditions E7 L21 3 # of occurences of event A ( ) total # of experiments P A

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Probability - review Probability - review Formal (Axiomatic) approach to assigning probability : 1. The probability of an event A: 2. The probability of the sample space S: 3. The probability of the complement of A: (A c : set of outcomes that are not in A) E7 L21 4 0 ( ) 1 P A ≤ ≤ ( ) 1 P S = ( ) 1 ( ) c P A P A = - A A c S
Probability - review Probability - review Formal (Axiomatic) approach to assigning probability : 1. The probability of B ,  ( B : set of outcomes in both and B)  and are mutually exclusive: and are independent : E7 L21 5 P(A  B ) = P(A)  ×  P(B) P(A  B ) = 0 A B S A B S

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Probability - review Probability - review Formal (Axiomatic) approach to assigning probability : 1. The probability of U B ,  ( U : set of outcomes in or or both and are mutually exclusive : and are not mutually exclusive : E7 L21 6 A B S P(A  U B ) = P(A) +  P(B) P(A  U B ) = P(A) +  P(B) - P(A  B )  A B S
Discrete random variable Discrete random variable Given a sample Space S a random variable is a function that assigns to each outcome a unique numerical value. Example: throwing of a dice once E7 L21 7 S = { } 1,2,3,4,5,6 X { } =

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Discrete random variable Discrete random variable Example: throwing of a dice once In this case, the random variable  X  only takes discrete values The random variable  X  is defined by the probability mass function E7 L21 8 { } 1,2,3,4,5,6 i x S = { } = ( ) ( ) i i P x P X x = = the probability that, after throwing a dice, X will be equal to x i
Discrete random variable Discrete random variable For a fair dice ,

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## This note was uploaded on 09/17/2011 for the course ENGINEERIN 7 taught by Professor Patzek during the Spring '08 term at Berkeley.

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Lecture_21_E7_L21_Statistics_F07-1 - 1 E7: INTRODUCTION TO...

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