Week2 - Stat231 William Marshall Stat231 William Marshall...

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Unformatted text preview: Stat231 William Marshall Stat231 William Marshall May 10, 2010 Stat231 William Marshall Week 2 Goals: Connect probability models to PPDAC Review discrete probability models (STAT 230) Stat231 William Marshall Random Variables Random Variable A number whose value is determined by chance A function from the sample space of an experiment to the real numbers The set of possible values of a random variable (S) is called its support Probability mass function f ( y ) = P ( Y = y ) , y S f ( y ) 1 y y f ( y ) = 1 Stat231 William Marshall Independence If you have two random variables, X and Y The conditional distribution of Y given X is f ( y | x ) = f ( x , y ) f X ( x ) The random variables are independent if and only if f ( x , y ) = f X ( x ) f Y ( y ) ( x , y ) Equivalently, if f ( y | x ) = f Y ( y ) Stat231 William Marshall Expected Value The expected value of a discrete random variable is E ( Y ) = X y yf ( y ) Variance of a random variable Var ( Y ) = E ( Y- E ( Y )) 2 The standard deviation is the square root of the variance sd ( Y ) = p Var ( Y ) Covariance of two random variables Cov ( X , Y ) = E [( Y- E ( Y ))( X- E ( X ))] Stat231...
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This note was uploaded on 11/21/2011 for the course MATH STAT 231 taught by Professor Marsh during the Spring '10 term at Waterloo.

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Week2 - Stat231 William Marshall Stat231 William Marshall...

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