7. [25 points] The passenger\'s perspective: Based on data collected by the U.S.

Question

7. [25 points] The passenger's perspective: Based on data collected by the U.S. Department of Transportation from 2010-2016, each year there were (approximately) 600,000,000 boarded passengers ·440,000 voluntary denied boarding passengers . 60,000 involuntary denied boarding passengers While these aggregate statistics are useful, we want to better describe the experience of an individual airline passenger: "How likely am I to be bumped? To do so, we model being bumped from a flight as a sequence of ii.d. Bernoulli random variables, B, B2. where B, = 1 if I am bumped and 0 otherwise. (We ignore voluntary denied boarding.) In parts (a)-(d) we first use the data above to parameterize the model (i.e., find P (B 1) (a) [1 point] How many passengers were involuntarily denied boarding for every 100,000 (b) [1 point] Assume that all flights have 200 seats and each flight has either 1 or 0 invol Then, in parts (e)-(g) analyze the model. passengers who boarded? untary denied boarding passenger with probability p. Find the value of p so that the expected number of involuntary denied boarding passengers over 500 flights matches your answer in (a) (c) [1 point] Suppose you are a passenger on one of these fights. Given that your flight is overbooked (i.e., there are 201 ticketed passengers for 200 seats), and assuming each passenger is equally likely to be bumped by the airline, what is the probability that you are bumped? (d) [1 point] From (b) and (c), what is the probability that you are bumped from a flight? (e) (7 points) Let R be the number of flights you take before the first flight you are bumped from, what is the distribution of R? Calculate and interpret ERI (f) [8 points) Assume (and specify) some reasonable number of flights you year. What is the probability you are bumped from a fight in the next 5 years? Th next 10 years? (8) (6 points] State three model assumptions that you think are unrealistic and a brief explanation (one sentence) for each

Explanation / Answer

According to Chegg policies, I am supposed to answer only first four parts of the question.

(a)

For 600,000,000 boarded passengers, 60,000 were involuntary denied.

Hence, for every 100,000 boarded passengers, (60,000/6,000) = 10 were denied boarding involuntarily.

(b)

Total seats = 200*500 = 100,000

p = 10/100000 = 0.0001

(c)

Probability of me getting bumped = 1 - (Number of seats / Number of total bookings)

= 1 - (200/201)

=1/201

(d)

Probability of NOT getting bumped = (200/201) * 0.9999 = 0.995

probability of getting bumped = 1 - 0.995 = 0.005

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