STA3007_0506_t01

STA3007_0506_t01 - STA 3007 Applied Probability Tutorial 1...

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STA 3007 Applied Probability 2005 Tutorial 1 1. Review on Probability (a) Discrete Probability Distributions p X ( x ) = Pr { X = x } i. p X ( x ) 0 ii. x p X ( x ) = 1 (b) Joint Probability Mass Function (Discrete) p XY ( x, y ) = Pr { X = x, Y = y } i. p XY ( x, y ) 0 ii. x y p XY ( x, y ) = 1 (c) Conditional Probability P ( A | B ) = P ( A and B ) P ( B ) i. P ( B ) > 0 (d) Conditional Probability Mass Function p X | Y ( x | y ) = p XY ( x,y ) p Y ( y ) i. p Y ( y ) > 0 (e) Marginal Probability Mass Function of X p X ( x ) = y p XY ( x, y ) (f) Law of Total Probability P ( B ) = i =1 P ( B | A i ) P ( A i ) p X ( x ) = y p XY ( x, y ) (Marginal pmf) p XY ( x, y ) = p X | Y ( x | y ) p Y ( y ) (Conditional Probability) p X ( x ) = y p X | Y ( x | y ) p Y ( y ) 1
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Exercises: i. Random Variables X and Y are independent and have the prob- ability mass functions: p X (0) = 1 2 p X (3) = 1 2 p Y (1) = 1 6 p Y (2) = 1 3 p Y (3) = 1 2 1.Determine the probability mass function of the sum Z=X+Y
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This note was uploaded on 05/21/2011 for the course STA 3007 taught by Professor Kb during the Spring '11 term at CUHK.

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STA3007_0506_t01 - STA 3007 Applied Probability Tutorial 1...

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