Hey all. Here's another I can't get.
The life, X in years of a car part had pdf:
f(x)= 3x² / 7³ * e^-(x/7)³ ; 0 < x < infinity
a) probability that this regulator will last at least 7 years?
b) Given that it lasts 7 yrs, conditional prob. that it will last at least another 3.5 yrs?
So for a, I got the correct answer by saying p(x>=7) = 1-p(x<=7)
And integrating f(x) from 0--->7
The answer is 0.368
Now for b, would I say 1-integral from 7--> 10.5? Cuz' that's what I was thinking, but it didn't work out. Please explain!