A statistical model uses a set of math equations to describe the behavior of something in
terms of random variables and probability.
Thus the most efficient estimate of the value of E -LCB- U (t)-RCB-, the trend rate, is the mean
value of the random variable given previously as
On the other hand, the distribution
of the random variable L = g (X), depends on the specific shape of the density function and so will generally differ from distribution to distribution.
To determine the actuarial present value of the benefit we need to calculate the expected value E (Z)-LCB- \ displaystyle \, E (Z)
-RCB- of this random variable Z. Suppose the death benefit is payable at the end of year of death.