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.

0.525 = 52.5%

Step-by-step 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

last option: rhombus or kite

step-by-step explanation:

a kite and rhombus have the same shape. as we don't have any specific formula for the calculation of area of kite. the diagonals are used to calculate the area of a kite or rhombus.

the formula for area of rhombus is given by:

here, d_1 is the first diagonal and d_2 is the second diagonal.

so,

last option is the correct answer ..

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