Answer:
(A) The expected loss is $5 million.
(B) The variance and standard deviation of physical damage loss are $225 million and $15 million respectively.
Step-by-step explanation:
The annual probability of Scary Airline's jets being destroyed is 1 in 10 million, i.e 0.0000001.
It is assumed that the jet is either destroyed or there was no loss suffered.
The loss amount in case the jet is destroyed is, $50 million.
(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)\\=($50\times 0.0000001)\ million+($0\times 0.9999999)\ million\\=\$5\ million[/tex]
Thus, the expected loss is $5 million.
(B)
The variance of a random variable X is: Var (X) = E (X²) - [E (X)]².
Compute the variance as follows:
[tex]Var(X)=E(X^{2})-[E(X)]^{2}\\=[\sum x^{2}P(X)-(5)^{2}]\ million\\=[($50^{2}\times 0.0000001)+($0\times 0.9999999)-25]\ million\\=[250-25]\ million\\=\$225\ million[/tex]
The standard deviation of physical damage loss is:
[tex]SD(X)=\sqrt{Var(A)}=\sqrt{225\ million}=\$15\ million[/tex]
Thus, the variance and standard deviation of physical damage loss are $225 million and $15 million respectively.
