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Exponential distribution, memory

  1. Feb 5, 2014 #1
    I am told that an exponential distribution is memoryless. But why aren't other distributions, such as the normal distribution, also memoryless? If I pick a random number from an exponential distribution, it is not effected by previously chosen random numbers. But isn't that also the case for a normal distribution, for example?

    What do I misunderstand?

    Thank you
     
  2. jcsd
  3. Feb 5, 2014 #2
    I think when people say the exponential distribution is memoryless, they mean that, for any exponentially distributed random variable [itex]X[/itex], the distribution of [itex]X-x[/itex] conditional on the event [itex]\{X\geq x\}[/itex] is the same as the distribution of [itex]X[/itex].

    It's easy to check that that the normal distribution (or, in fact, anything that can take on negative values) can't satisfy the above property.
     
  4. Feb 5, 2014 #3

    statdad

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    Homework Helper

    The memory less notion refers to the fact that for any positive numbers s and t

    [tex]
    P(X > s + t | X > t) = P(X > s)
    [/tex]

    It can be shown that this property gives the exponential distribution as the unique continuous distribution with the property.
     
  5. Feb 5, 2014 #4
    Thank you
     
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