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Math Help - Continuous uniform distribution

  1. #1
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    Cool Continuous uniform distribution

    Pls explain the following question, what they are really asking for and give the solution for it?
    ********************
    The uniform steel bar was loaded until it broke. The loaded length of bar was 240mm.
    (a) Find the probability that the break did not lie in the middle third of the bar.
    (b) If x is the distance in from the end of the bar at which it broke, find E(X) and Var(X)
    *************************
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  2. #2
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    Quote Originally Posted by Sashikala View Post
    Pls explain the following question, what they are really asking for and give the solution for it?
    ********************
    The uniform steel bar was loaded until it broke. The loaded length of bar was 240mm.
    (a) Find the probability that the break did not lie in the middle third of the bar.
    (b) If x is the distance in from the end of the bar at which it broke, find E(X) and Var(X)
    *************************
    I don't believe that there is enough information here to answer that question. What causes the bar to break? Is the bar "simply" supported at the two ends or otherwise?

    This problem may be assuming that the point of breaking is uniformly distributed- in that case, it is possible to answer the questions but that is certainly not stated in the problem.
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  3. #3
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    Continuous uniform distribution

    It is the Q4 of Pg76 from Statistics 2 (Heinemann). There is no further information. We may have to do some assumption. The answers are listed as follows: for (a) 2/3 (b)120mm,4800 mm2.
    If you are able to arrive at the answers with the assumption you mentioned, pls do explain it with the sketch of pdf as I do not understand the question as such.
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  4. #4
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    Quote Originally Posted by Sashikala View Post
    Pls explain the following question, what they are really asking for and give the solution for it?
    ********************
    The uniform steel bar was loaded until it broke. The loaded length of bar was 240mm.
    (a) Find the probability that the break did not lie in the middle third of the bar.
    (b) If x is the distance in from the end of the bar at which it broke, find E(X) and Var(X)
    *************************
    Quote Originally Posted by Sashikala View Post
    It is the Q4 of Pg76 from Statistics 2 (Heinemann). There is no further information. We may have to do some assumption. The answers are listed as follows: for (a) 2/3 (b)120mm,4800 mm2.
    If you are able to arrive at the answers with the assumption you mentioned, pls do explain it with the sketch of pdf as I do not understand the question as such.
    (a) The break obviously occurs in either the first, middle or end third of the bar ....

    (b) You'd expect the average distance to be one half the length of the bar ....

    Aside: Interestingly, the average length of the smaller piece is NOT 120mm, it's 60mm ....
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  5. #5
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    Cool Continuous uniform distribution

    I got the answers for part (b).
    Can you pls show the working for Part(a).
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  6. #6
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    Quote Originally Posted by Sashikala View Post
    I got the answers for part (b).
    Can you pls show the working for Part(a).
    From what I posted plus the known answer, there is no further working required .... Think about it.
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  7. #7
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    Thumbs up Continuous uniform distribution

    Hi, Mr Fantastic
    I got the answer for part(a) as well.
    Thanks for the tip you gave.
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