If you have any shortcuts to save time during the test, please share. Here are a few of mine:
This one saves from messy integration by parts, which I discovered on accident...
If a policy limit L is applied to an EXPONENTIAL distribution, the new mean is the old mean (theta) multiplied by the probability that X<L.
If a deductible D is applied to an exponential distribution, the new mean is the old mean multiplied by the probability that X>D.
These formulas, shown below, can also be used to find the deductibles or limits needed to alter the means.
Let u=original mean (theta); v=new mean after L or D is enforced...
Thus if we want the expected claim payment to be 20% less than the $500 mean damage distributed exponentially by adding either a limit or deductible...
New expected claim payment = 400
400 = 500(1-e^(-L/500))
Thus L = $804.72
400 = 500(e^(-D/500)
Thus D = $111.57
If X and Y follow independent exponential distributions with means 2 and 3, what is the probability Y<X? (And for other multivariate distributions...)
If the answers are separated by more than 3% or so, instead of double integrating the joint density function, a quick glance at the normal distribution table seems appropriate, no?
(I'm assuming that this table is the one and only information that will be provided during the test???? Anyone know?)