contnotes

contnotes - Continuous Random Variables De.nitions/Notes...

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Continuous Random Variables – De…nitions/Notes De…nition 1 A random variable X is said to be continuous if its set of possible values is an entire interval of numbers – that is, if for some A < B , any number x between A and B is possible. De…nition 2 Let X be a continuous random variable. Then a probability distribution or probability density function (pdf) of X is a function f ( x ) such that for any two numbers a and b with a · b : P ( a · X · b ) = Z b a f ( x ) dx: That is, the probability that X takes on a value in the interval [ a;b ] is the area under the graph of the density function. The graph of f ( x ) is often referred to as the density curve . Conditions For f ( x ) to be a legitimate pdf, it must satisfy the following two conditions: 1. f ( x ) ¸ 0 for all x: 2. R 1 ¡1 f ( x ) dx = 1 : De…nition 3 A continuous random variable X is said to have a uniform distribution on the interval [ A;B ] if the pdf of X is: f ( x ; A;B ) = ( 1 B ¡ A A · x · B 0 otherwise
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This note was uploaded on 01/08/2012 for the course EXST 4050 taught by Professor Staff during the Fall '10 term at LSU.

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contnotes - Continuous Random Variables De.nitions/Notes...

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