Problem 4E

A frequent force of mortality used in actuarial science is λ(w) = aebw + c. Find the cdf and pdf associated with this Makeham’s law.

Answer:

Step 1 of 1 :

Since a frequent force of mortality used in actuarial science is

Our goal is to find

The cdf and pdf associated with this Makeham’s law.

Now we have to find the conditional distribution function and probability distribution function

We know that

The function H will be given by,

Therefore

Here

The conditional distribution function is

The probability distribution function is

Hence we have proved the conditional distribution function and probability distribution function.