100AFinal Review

100AFinal Review - STAT 100A Review for final 1 Part I:...

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Unformatted text preview: STAT 100A Review for final 1 Part I: study one random variable at a time A discrete random variable X takes values in a discrete list { x 1 ,x 2 ,... } . Its behavior is governed by a probability mass function p ( x ) for x = { x 1 ,x 2 ,... } , so that P ( X = x ) = p ( x ) or P ( X = x i ) = p i , where p i 0 and i p i = 1. We can use the following table to represent the probability mass function p ( x ): x x 1 x 2 ... x i ... p ( x ) p 1 p 2 ... p i ... For any statement about the random variable, the probability can be calculated from the probability mass function. For example, P ( X ( a,b )) = x ( a,b ) p ( x ). A continuous random variable X takes values in a continuous interval. Its behavior is governed by a probability density function f ( x ) = P ( X ( x,x + x )) / x , where x is infinitesimal. R f ( x ) dx = 1. For an interval ( a,b ), P ( X ( a,b )) = R b a f ( x ) dx . We can imagine that X is the horizontal coordinate of a random point in the area under f ( x ). P ( X ( a,b )) is the area between a and b under f ( x ). The cumulative density function F ( x ) = R x- f ( t ) dt . F ( x ) = f ( x ). 2 Part II: study two random variables together If ( X,Y ) is a pair of discrete random variables, their joint probability mass function p ( x,y ) = P ( X = x Y = y...
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100AFinal Review - STAT 100A Review for final 1 Part I:...

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