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Math Help - Help needed please! probability distributions

  1. #1
    Junior Member Ruichan's Avatar
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    Help needed please! probability distributions

    1. The time (in hours) required to repair a machine is an exponentially distributed random variablewith parameter λ = 1/4.
    (a) What is the probability that a repair time exceeds 4 hours.
    (b) What is the conditional probability that a repair takes at least 10 hours, given that its duration exceed 9 hours.

    For a) I got the answer 1 - e^{-1}

    How do you do b)?
    Is it P(X>=10) = 1 - P(X<=9)?


    2. An electronic equipment is used to measure brain mass. If the brain mass for a randomly selected person is m grams, the machine measures and amount Y , where Y = m + X and X is normally distributed with mean 0 and variance 4. What is the probability that the measure Y does not deviate from the true value m by more than 1.3 grams?

    Thank you very much!
    Last edited by CaptainBlack; November 28th 2006 at 07:58 PM.
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  2. #2
    Junior Member F.A.P's Avatar
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    Quote Originally Posted by Ruichan View Post
    1. The time (in hours) required to repair a machine is an exponentially distributed random variablewith parameter λ = 1/4.
    (a) What is the probability that a repair time exceeds 4 hours.
    (b) What is the conditional probability that a repair takes at least 10 hours, given that its duration exceed 9 hours.

    For a) I got the answer 1 - e^{-1}

    How do you do b)?
    Is it P(X>=10) = 1 - P(X<=9)?

    Thank you very much!
    (a) Let T be the time until finished repair. Then T is Exp(1/4) and has CDF

    P(T<t) = 1 - e^{-t/4}

    Probability that a repair exceeds t hours is then
    P(T>t) = 1 - P(T<t) = e^{-t/4}

    (b) Using the definition of conditional probability we get, for 0 < s < t

    P(T>t|T>s) = P(T>t,T>s)/P(T>s) = P(T>t)/P(T>s) =

    = e^{-(t-s)/4}
    Last edited by F.A.P; December 21st 2006 at 09:15 AM.
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