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Unformatted text preview: 0. Also, the parameter is a positive real number. The exponential r.v. is often used as the distribution for the time required to complete a certain task or for the elapsed time between successive occurrences of a specified event. CDF: = ) ( x F X 0 for x 0. x X e x F = 1 ) ( for x > 0. Mean: 1 Variance: 2 1 Special Property 1: Memorylessness: If X is exponentially distributed, then its conditional probability obeys the following property: s t X P + > ( X > s) = P(X > t) for all s, t 0. Example numbers: P(X>50 X>35) = P(X > 15). Special Property 2: Tail Probability Function: If X is exponentially distributed, then we have a specific formula for X > x. x x X e e x F CDF x X P = = = = > ) 1 ( 1 ) ( 1 1 ) ( . Say X is exponentially distributed with lambda equal to 10. Then, P(X>50 X>35) is 150 e ....
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- Spring '08