# Thread: help with a tricky question

1. ## 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

2. ## 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

3. ## Re: help with a tricky question

Originally Posted by BGM
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

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

4. ## Re: help with a tricky question

Do you know what the distribution of the sum of two normal random variables is?

5. ## 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.

6. ## Re: help with a tricky question

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

7. ## Re: help with a tricky question

Originally Posted by BGM
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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