Answer:
(A) The expected loss is $0.045.
(B) The variance and standard deviation of physical damage loss are $2,025 and $45 respectively.
Step-by-step explanation:
The annual probability of Bespin Car Rental's cars being destroyed is 1 in a million, i.e 0.000001.
It is assumed that the car is either destroyed or there was no loss suffered.
The loss amount in case the car is destroyed is, $45,000.
(A)
The distribution for physical damage loss is displayed in the table below.
The Expected value of physical damage loss is:
[tex]E(X)=\sum xP(X)=(45000\times0.000001)+(0\times0.999999)=0.045[/tex]
Thus, the expected loss is $0.045.
(B)
The variance of a random variable X is: Var (X) = E (X²) - [E (X)]².
The variance of physical damage loss is:
Compute the variance as follows:
[tex]Var(X)=E(X^{2})-[E(X)]^{2}\\=\sum x^{2}P(X)-[\sum xP(X)]^{2}\\=[(45000^{2}\times0.000001)+(0^{2}\times0.999999)]-(0.045)^{2}\\=2025-0.002025\\=2024.997975\\\approx2025[/tex]
The standard deviation of physical damage loss is:
[tex]SD=\sqrt{Var(X)}=\sqrt{2025}=45[/tex]
Thus, the variance and standard deviation of physical damage loss are $2,025 and $45 respectively.
