# help with a tricky question

#### MFM

##### New Member
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

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#### BGM

##### TS Contributor
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

[math] D + L - R [/math]

#### MFM

##### New Member
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

[math] D + L - R [/math]
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

#### Dason

##### Ambassador to the humans
Do you know what the distribution of the sum of two normal random variables is?

#### MFM

##### New Member
Do you know what the distribution of the sum of two normal random variables is?
i guess it will be normal distribution also

#### MFM

##### New Member
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_distribution#Combination_of_two_independent_random_variables
http://en.wikipedia.org/wiki/Multivariate_normal#Affine_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 ?