An airline charges the following baggage fees: $25 for the first bag and $35 for

Question

An airline charges the following baggage fees: $25 for the first bag and $35 for the second. Suppose, 54% of passengers have on checked luggage, 34% have one piece of checked luggage and 12% have two pieces a negligible portion of people check more than two bags. The number of checked luggage for a given passenger may be considered a random process. (a) For this process, show the possible outcomes and their corresponding probabilities. (b) Show that revenue is a random variable which assigns a value to each possible outcome. (c) Compute the expectation value for this random variable. (d) Compute the standard deviation for this random variable. (e) About how much revenue should the airline expect for a flight of 120 passengers?

Explanation / Answer

a) here random variable X is number of checked luggage with 3 possible outcomes

P(X=0)=0.54

P(X=1)=0.34

P(X=2)=0.12

b)Revenue R

R(X=0)=0

R(X=1)=25

R(X=2)=25+35=60

c) E(R) =0.54*0+0.34*25+0.12*60=$15.7

d)E(R2) =0.54*02+0.34*252+0.12*602=644.5

hence std deviation =(644.5-15.72)1/2 =19.95

e)expected revenue =120*15.7=1884

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