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Math Help - Exponential Distribution

  1. #1
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    Exponential Distribution

    For a certain type of electrical component, the lifetime X (in thousands of hours) has an Exponential
    distribution with rate parameter lambda  = 0.5. What is the probability that a new component will last
    longer than 1000 hours? If a component has already lasted 1000 hours, what is the probability that
    it will last at least 1000 hours more?


    Can anyone help with this question?
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  2. #2
    Senior Member MacstersUndead's Avatar
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    Re: Exponential Distribution

    Let lambda = t

    For (a) we are asked to calculate P(X>1) = 1 - P(X<1) but we know what the CDF of a exponential distribution is, so
    P(X>1) = 1 - (1 - e^{-.5(1)} = e^{-.5} =  .61

    For (b), we are asked to calculate P(X>2|X>1) = \frac{P(X>2 and X>1)}{P(X>1)} = \frac{P(X>2)}{P(X>1)}. I'll leave the rest up to you
    Last edited by MacstersUndead; March 3rd 2013 at 11:08 AM.
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    Re: Exponential Distribution

    thank you
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