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    help with a tricky question




    hi guys,
    when i was looking for statistics exams to practice i found this problem at mit final exam back at 2004

    the condition for failure of a column is given by D +L > R , where D is the dead load, L is the live load , and R is the resistance, all expressed in the same units .
    suppose that D, L and R are independent normally distributed variables with the following distributions :
    D ~ N(100,25^2) , L ~ N(150,50^2) and R ~ N(300,20^2)
    Find the probability of failure of the column

    Now is this question is one function in two random variables or its multiple random variables and how to solve it .

    thanks guys
    Last edited by MFM; 04-22-2014 at 12:27 PM.

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    Re: help with a tricky question

    In general, when you are calculating the probability of an event involving multiple random variables, you need to make use of their joint distribution (which is multivariate normal in this case).

    However, in this case you do not need to consider that. Do you know the distribution of

    D + L - R

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    Re: help with a tricky question

    Quote Originally Posted by BGM View Post
    In general, when you are calculating the probability of an event involving multiple random variables, you need to make use of their joint distribution (which is multivariate normal in this case).

    However, in this case you do not need to consider that. Do you know the distribution of

    D + L - R
    no i dont all i know that each one is normally distributed with their parameters
    and about their joint distribution means that f(d)f(l)f(r) cause their independent

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    Re: help with a tricky question

    Do you know what the distribution of the sum of two normal random variables is?
    I don't have emotions and sometimes that makes me very sad.

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    Re: help with a tricky question

    If you do not know/learn that yet, probably you need to learn more to tackle this. This is the basic requirement of this question.

    For your curiosity, you may check these out:

    http://en.wikipedia.org/wiki/Normal_...ndom_variables
    http://en.wikipedia.org/wiki/Multiva...transformation

    Basically it said that the linear combinations of independent normal random variables is still normally distributed.

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    Re: help with a tricky question

    Quote Originally Posted by Dason View Post
    Do you know what the distribution of the sum of two normal random variables is?
    i guess it will be normal distribution also

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    Re: help with a tricky question


    Quote Originally Posted by BGM View Post
    If you do not know/learn that yet, probably you need to learn more to tackle this. This is the basic requirement of this question.

    For your curiosity, you may check these out:

    http://en.wikipedia.org/wiki/Normal_...ndom_variables
    http://en.wikipedia.org/wiki/Multiva...transformation


    Basically it said that the linear combinations of independent normal random variables is still normally distributed.
    okay so how to Find the probability of failure of the column ?

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