Answer:
b = 450
Step-by-step 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:
[tex]f = \dfrac{1}{b}...... since \ \ \ 0 \leq x \leq b[/tex]
[tex]E(x) = P[X<180] \ E|X|X<180]+P[X \geq 180] \ E{|X| X \geq 180][/tex]
[tex]E(x) = \dfrac{180}{b}(90) + [1-\dfrac{180}{b}](180)[/tex]
we know that E(x) = 144
thus;
[tex]144= \dfrac{180}{b}(90) + [1-\dfrac{180}{b}](180)[/tex]
[tex]144= \dfrac{16200}{b} + 180 -\dfrac{32400}{b}[/tex]
[tex]144- 180= \dfrac{16200}{b} -\dfrac{32400}{b}[/tex]
[tex]-36= \dfrac{16200}{b} -\dfrac{32400}{b}[/tex]
[tex]-36= \dfrac{16200-32400}{b}[/tex]
[tex]-36= \dfrac{-16200}{b}[/tex]
-36 b = -16200
b = -16200/-36
b = 450
