When this posts I should be just getting home from Nepal (jet lag is no place to write posts). So, this post and the next couple are homework for you. Take a look, work the problem, solve it, then show your work. Comment with why you chose your response and why you didn’t select one of the others.
From question 19 of ASQ CRE 2009 sample exam.
19. In the model y = 12.1x1 + 5.3x2 + å, the x1 follows a Weibull distribution with a shape parameter of 3.5 and a characteristic life of 20; x2 follows a lognormal distribution with a mean of 16 and a standard deviation (ó) of 2.5; and å is a random variable with a mean of 0 and a ó of 1. In this situation, which of the following methods would be best to evaluate the distribution of y?
(B) Monte Carlo simulation
(D) Numerical integral
Best means this one is subjective (never did like this type of question) and it provides a great start to a discussion on why you select your answer. Please comment and defend your selection.
Related:
Basic Statistics (article)
First 5 Questions (article)
Sample Size – success testing (article)
I would go with Monte Carlo Simulations. Reason being that we are adding 3 random variable with different underlying distributions. Using Monte Carlo Simulations it would be easier (at least for me)to compute the RHS and then perform a goodness of fit on the resulting values of y to determine its distribution
Hi Bilal,
Thanks for the comment. Yes Monte Carlo maybe the easiest approach. When possible I do like closed form solutions, yet that is not always possible.
Cheers,
Fred