elemprob-fall2010-page31

elemprob-fall2010-page31 - and integrate. In particular,...

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and integrate. In particular, for x , large, P ( Z x ) = 1 - Φ( x ) 1 2 π 1 x e - x 2 / 2 e - x 2 / 2 . 13 Some continuous distributions We look at some other continuous random variables besides normals. Uniform . Here f ( x ) = 1 / ( b - a ) if a x b and 0 otherwise. To compute expectations, E X = 1 b - a R b a xdx = ( a + b ) / 2. Exponential . An exponential with parameter λ has density f ( x ) = λe - λx if x 0 and 0 otherwise. We have P ( X > a ) = R a λe - λx dx = e - λa and we readily compute E X = 1 , Var X = 1 2 . Examples where an exponential random variable is a good model is the length of a telephone call, the length of time before someone arrives at a bank, the length of time before a light bulb burns out. Exponentials are memory-less. This means that
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This note was uploaded on 12/29/2011 for the course MATH 316 taught by Professor Ansan during the Spring '10 term at SUNY Stony Brook.

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