Question

The moment generating function for health care costs experienced by a policyholder is given as follows:

Mx(t)= (4/4-t)^3

An insurer reimburses the policyholder for 70% of health care costs experienced by the policyholder. Calculate the expected reimbursement by the insurer for a policyholder.

Answer 1

0.525 = 52.5%

Explanation:

Moment generating function ( Mx(t) ) = ( 4 / 4-t)^3

Reimbursement by Insurer = 70%

Determine the expected reimbursement by insurer for policyholder

d/dx (Mx(t) ) = d/dt ( 4 / 4-t)^3 = d/dt (1 - t/4 )^-3

= 3/4 ( 1 - t/4 )^-4 = 3/4

as t → 0

Given that the insurer reimburses 70% = 0.7

expected reimbursement = 0.7 * 3/4 = 0.7 * 0.75 = 0.525