MACROMICRO & AG FIN
MACROMICRO & AG FIN AEB 6933
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This 2 page Class Notes was uploaded by Weldon Rau I on Friday September 18, 2015. The Class Notes belongs to AEB 6933 at University of Florida taught by Charles Moss in Fall. Since its upload, it has received 28 views. For similar materials see /class/206590/aeb-6933-university-of-florida in Agricultural Economics And Business at University of Florida.
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Date Created: 09/18/15
Binomial Random and Normal Random Variables Lecture XI I Bernoulli Random Variables A The Bernoulli distribution characterizes the coin toss Speci cally there are two events X 01 with X 1 occurring with probability p The probability distribution function PX can be written as X 17 PX p 1 p B Next we need to develop the probability of XY where both X and Y are identically distributed If the two events are independent the probability becomes PlXaY PXPYl My 1PH1Pl y If 1 12 C Now this density function is only concerned with three outcomes Z XY012 1 There is only one way each for Z 0 or Z 2 a Speci cally for Z 0 X 0 and Y 0 b SimilarlyforZ2X1andY1 2 However for Z 1 either Xl and Y0 or X0 or Yl Thus we can derive PZ 0 p0 1 190 PZ 1PX1Y 0PX0Y1 p10 1p210 po11p201 2pl1 p1 PZ2p2l p0 D Next we expand the distribution to three independent Bernoulli events where Z WXY0123 PZ PWXY PlWlPlePlYl pwpxpy 1 plew 1 17er 1 pley pwxy 1p3iwerey pz 1 p372
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