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Unformatted text preview: its a good choice a lot of the time. What is the distinction between the inverse transform method and saying Q ( v ) = P ( u ) | du dv | , then computing the derivative and plugging in, where P ( u ) is uniform? Is this the same thing? No, this expression cant be used directly for the problem were trying to solve. We know Q ( v ): its the function we are trying to pick values from. If u is a uniform variable, P ( u ) is just a constant, 1 / ( b-a ), where [ a,b ] is the interval we are selecting over, and its just 1 for [0 , 1]. Selecting u and plugging in to Q ( v ) = | du dv | is just going to give values of Q ( v ), not variables v distributed according to Q ( v ). But if you integrate Q ( v ) = | dF dv | (writing u ( v ) = F ( v )), you get the expression relating the value of uniformly-selected u to Q ( v ): this is the inverse transform expression u = R v F ( v ) dv . Then v = F-1 ( u ) will have the distribution you want....
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This note was uploaded on 01/16/2012 for the course PHYSICS 392 taught by Professor Scholberg during the Fall '11 term at Duke.
- Fall '11