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# Chapter03_answer - Random Variables A random variable is a...

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Random Variables random variable  is a function which maps each  element in the sample space of a random process to a  numerical value. discrete random variable  takes on a finite or  countable number of values. We will identify the distribution of a discrete random  variable  X  by its  probability mass function (pmf) f X (x) =  P ( X  =  x ).  Requirements of a pmf: f ( x  0 for all possible  x –   all  ( ) 1 x f x =

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Cumulative Distribution Function The  cumulative distribution function   (cdf)    is given by An increasing function starting from a value of 0 and  ending at a value of 1. When we specify a pmf or cdf, we are in essence  choosing a  probability model  for our random  variable. all  ( )    ( ) ( ) t x F x P X x f t = =
Reliability example Consider the series system with three independent  components each with reliability  p . Let  X i  be 1 if the  i th component works (S) and 0  if it fails  (F). X i  is called a  Bernoulli random variable . Let  f Xi (x) =  P ( X i  =  x ) be the pmf for  X i .

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Chapter03_answer - Random Variables A random variable is a...

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