UCR SOC 005 STAT SPR 2010 Session 14 V2

UCR SOC 005 STAT SPR 2010 Session 14 V2 -...

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THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of   Mississippi Institute for Advanced Education in Geospatial Science Session 14 Wednesday, 28 April 2010 David Swanson Watkins 1223 David.swanson@ucr.edu SOCIOLOGY 005  STATISTICAL ANALYSIS
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THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of   Mississippi Institute for Advanced Education in Geospatial Science Today’s Schedule Turn in Assignment 2    Probability and Its Measurement
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THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of   Mississippi Institute for Advanced Education in Geospatial Science Probability Distributions What is a probability distribution? First recall that in this class we are using  the ‘relative frequency’ definition of  probability.   There are two fundamental types,  discrete (nominal, ordinal) and  continuous (ratio, interval) In a discrete probability distribution, 
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THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of   Mississippi Institute for Advanced Education in Geospatial Science Probability Distributions If  a variable, ‘x,’ has a set of values, x 1 , x 2 , x 3 , …,x k , with probabilities p 1 , p 2 , p 3 ,…,p k where p 1 +p 2 +p 3 +,…,+p k  = 1.00, we can say  that a discrete probability distribution for x  has been defined.  The function p(x) which has the respective  values p 1 , p 2 , p 3 ,…,p for  x = x 1 , x 2 , x 3 ,…,x is called the probability  function or frequency function of x.
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THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of   Mississippi Institute for Advanced Education in Geospatial Science Probability Distributions An example.  Let a pair of (fair) dice be tossed and let  the sum of the points obtained be denoted by x.  Then the (discrete) probability distribution is x p(x) 2 1/36 3 2/36 4 3/36 5 4/36 6 5/36 7 6/36 8 5/36 9 4/36 10 3/36 11 2/36 12 1/36
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THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of   Mississippi Institute for Advanced Education in Geospatial Science Because x can assume certain values with given  probabilities, it is often called a discrete random  variable. This is analogous to a relative frequency  distribution with probabilities replacing relative  frequencies x p(x) 2 1/36 3 2/36 4 3/36 5 4/36 6 5/36 7 6/36 8 5/36 9 4/36 10 3/36 11 2/36 12 1/36
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THE UNIVERSITY OF CALIFORNIA RIVERSIDE The University of   Mississippi Institute for Advanced Education in Geospatial Science Probability Distributions The preceding ideas can be extended to the case  where a variable, ‘x,’ has a ‘continuous’ set of  values.   The relative frequencies of these  values becomes in the theoretical or limiting  case a continuous curve, whose equation is Y =  p(x)
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UCR SOC 005 STAT SPR 2010 Session 14 V2 -...

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