help with a tricky question

MFM

New Member
#1
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:

BGM

TS Contributor
#2
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
#3
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
 

BGM

TS Contributor
#5

MFM

New Member
#7
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 ?