claims Xi are iid with Exponential distribution with mean 10. What is the value of: P(X1 <= 15 and X1 + X2 <= 30) =? I am not exactly sure how to solve this. Integral from 0 to 15 for f(x1) dx multiplied by another integral from 15 to 30 for the f(x1+x2)? This question does not give an explicit solution and I am not able to confirm my approach.
I had a quick bash at this and I'm screwing up the algebra, but...the general approach: first develop a expression for P(X1=a, X1+X2=b) (or rather, the density, since it is continuous). Then integrate this expression over the set of points 0<a<15 and 0<b<30-a. The result is left as an exercise to the reader (!)
This was a bit of a pig and was repeated in September 2009 Q2 (yup - look far enough back and the questions do repeat). The key is to write each probability for one of the random variables: P(X1 <=15 and X2 <= 30 - X1) So we'll integrate over the X1 from 0 to 15 and over the X2 from 0 to 30-x1. Hope that helps
