Question

Amazon has three packages (Package A, Package B, and Package C) that is to be shipped to Bill’s address. Package A is worth $100, Package B is worth $200, and Package C is worth $300. All three packages have a 90% chance of arriving and a 10% chance of being lost in transit.

a. Set up a probability distribution with the appropriate probabilities for each possible outcome.

b. What is the expected loss (P*)?

c. How much risk does Amazon face in this delivery purchase. (i.e. –what is the coefficient of variation)?

Answer 1

a)

probabilty of A arrived P(A)=P(B)=P(C)=0.9

probabilty of A not arrived =P(NA)=P(NB)=P(NC)=0.1

here let Event 123 represnt happening of first event*second event*third event

hence below is the table for expected loss

EVENT	X	P(X)=P(first event*second event*third event)	XP(X)	X2 P(X)
A*B*C	0	0.729	0	0
NA*B*C	-100	0.081	-8.1	810
A*NB*C	-200	0.081	-16.2	3240
A*B*NC	-300	0.081	-24.3	7290
NA*NB*C	-400	0.009	-3.6	1440
A*NB*NC	-500	0.009	-4.5	2250
NA*B*NC	-600	0.009	-5.4	3240
NA*NB*NC	-700	0.001	-0.7	490
		TOTAL	-62.8	18760

b) expected loss =xP(x) = -62.8

c)

std deviation =(x²P(x)-xP(x)²)^1/2 =(18760-(-62.8)²)^1/2= 121.721

Coefficient of variation = (std deviation/mean)*100 = (121.721/-62.8)*100 = -193.82%