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Unformatted text preview: AMS 311 Joe Mitchell Review for Exam3 Main Topics : (1) Joint distributions, conditional density, conditional expectation • joint density of X and Y , f ( x, y ) (ALWAYS DRAW A PICTURE OF THE SUPPORT SET!); In discrete case, the joint mass function, p ( x, y ) = P ( X = x, Y = y ) • marginal density of X , f X ( x ) = integraltext ∞-∞ f ( x, y ) dy ; in discrete case, p X ( x ) = P ( X = x ) = ∑ y j p ( x, y j ) • conditional density of X given Y , f X | Y ( x | y ) = f ( x,y ) f Y ( y ) , defined only for values of y with f Y ( y ) > 0; understand how to use it to compute things like P ( X > a | Y = b ), E ( X 3 | Y = b ), etc; in the discrete case, we have conditional mass function, p X | Y ( x | y ) = P ( X = x | Y = y ). (2) Using conditioning to compute probabilities and expectations • Staged experiments: e.g., X is Uniform(3,4), then Y is chosen exponential with parameter X 2 , find E ( Y ), P ( Y > 7), etc....
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- Fall '08
- Probability theory, Joe Mitchell, discrete case