Question

For a certain health insurance policy, losses are uniformly distributed on the interval [0, b). The policy has a deductible of $180 and the expected value of the unreimbursed portion of a loss is $144. Calculate b.

Answer 1

b = 450

Explanation:

Given that:

for a certain health insurance policy; Losses are uniformly distributed on the interval (0, b)

If the policy has a deductible value of $180 &

the expected value of the unreimbursed portion of a loss E(x)= $144

Then; b whican be calculated as:

`f = (1)/(b)...... since \ \ \ 0 \leq x \leq b`

`E(x) = P[X<180] \ E|X|X<180]+P[X \geq 180] \ E{|X| X \geq 180]`

`E(x) = (180)/(b)(90) + [1-(180)/(b)](180)`

we know that E(x) = 144

thus;

`144= (180)/(b)(90) + [1-(180)/(b)](180)`

`144= (16200)/(b) + 180 -(32400)/(b)`

`144- 180= (16200)/(b) -(32400)/(b)`

`-36= (16200)/(b) -(32400)/(b)`

`-36= (16200-32400)/(b)`

`-36= (-16200)/(b)`

-36 b = -16200

b = -16200/-36

b = 450