Lecture23 - GEM2900 Understanding Uncertainty Statistical...

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GEM2900: Understanding Uncertainty & Statistical Thinking DSAP, NUS, Semester 1, 2008/2009 – 1 GEM2900: Understanding Uncertainty & Statistical Thinking Berwin Turlach [email protected] Department of Statistics and Applied Probability National University of Singapore
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Example GEM2900: Understanding Uncertainty & Statistical Thinking DSAP, NUS, Semester 1, 2008/2009 – 170 Suppose that 3 balls are randomly selected from an urn containing 2 red, 4 white and 4 blue balls. If we let X and Y denote, respectively, the number of red and white balls chosen, then the joint p.m.f. and the marginal p.m.f.s of X and Y are given by: Y 0 1 2 3 p X ( x ) 0 4 120 24 120 24 120 4 120 56 120 X 1 12 120 32 120 12 120 0 56 120 2 4 120 4 120 0 0 8 120 p Y ( y ) 20 120 60 120 36 120 4 120 1
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Independence of two (discrete) random variables GEM2900: Understanding Uncertainty & Statistical Thinking DSAP, NUS, Semester 1, 2008/2009 – 171 Two discrete random variables X and Y are said to be independent if for every pair of x and y values p X,Y ( x, y ) = p X ( x ) · p Y ( y ) Note that this is equivalent to P ( X = x, Y = y ) = P ( X = x ) · P ( Y = y ) for all x and y i.e. the events { X = x } and { Y = y } are independent for all possible values of x and y .
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