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Question

A Philadelphia taxi driver gets new customers at rate 1/5 per minute.
With probability 1/3 the person wants to go to the airport, a 20 minute trip.
After waiting in a line of cabs at the airport for an average of 35 minutes,
he gets another fare and spends 20 minutes driving back to drop that person
off. Each trip to or from the airport costs the customer a standard $28 charge
(ignore tipping). While in the city fares with probability 2/3 want a short trip
that lasts an amount of time uniformly distributed on [2, 10] minutes and the
cab driver earns an average of $1.33 a minute (i.e., 4/3 of a dollar). (a) In the
long run how much money does he make per hour? (b) What fraction of time
does he spend going to and from the airport (inducing the time spent in line
there)?
A Philadelphia taxi driver gets new customers at rate 1/5 per minute.
With probability 1/3 the person wants to go to the airport, a 20 minute trip.
After waiting in a line of cabs at the airport for an average of 35 minutes,
he gets another fare and spends 20 minutes driving back to drop that person
off. Each trip to or from the airport costs the customer a standard $28 charge
(ignore tipping). While in the city fares with probability 2/3 want a short trip
that lasts an amount of time uniformly distributed on [2, 10] minutes and the
cab driver earns an average of $1.33 a minute (i.e., 4/3 of a dollar). (a) In the
long run how much money does he make per hour? (b) What fraction of time
does he spend going to and from the airport (inducing the time spent in line
there)?

Solution

x)

= (xxxxxxxxxxy xxxx xx gets xx airport xxxx) * ((xxxxx Earnings)/(Total xxxx taken xx xxxxxxx)) = (1/3) * ((28*2) / (xx+xx+xx) )= =56/225=0.249

xxxx, Expected xxxxy xx xxxxx in xxxxxxx trips xxx xxxx=x.xxx*xx=$xx.xx =(xxxxxxxxxxy that xx gets x xxxxxx xxxy fare) * (Avg. xxxxy xx xxxxx in xxxxxx city xxxxx) = (x/x) * x.xx = x.xxx xxxxxxxx xxxxy he xxxxx in xxxxxx xxxy xxxxx per xxxx = x.xxx*xx = xx.x

b)

xxxxxxxx of xxxx xxxxx xxxxx to xxx from xxx xxxxxxx (xxxxxxxxx the xxxx spent xx xxxx xxxxx)

=((Probability xx airport xxxx) * (xxxx taken xx and xxx xxxxxxx))/ ((xxxxxxxxxxy of xxxxxxx trip) * (xxx. xxxx taken xx airport xxxxx))+((xxxxxxxxxxy xx xxxy trip) *(xxx. time xxxxx xx xxxy trips))

= (1/3)*(20+20)/(((1/3)*(20+35+20))+((2/3)*((2+10)/2))))

=xx/(xx+xx+xx+xx)=xx/xx=x.xx xxxxx, xx spends xx% of xxxx xx x day xxxxxxx to xxx xxxx xxx airport

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Payment
A Philadelphia taxi driver gets new customers at rate 1/5 per minute.
With probability 1/3 the person wants to go to the airport, a 20 minute trip.
After waiting in a line of cabs at the airport for an average of 35 minutes,
he gets another fare and spends 20 minutes driving back to drop that person
off. Each trip to or from the airport costs the customer a standard $28 charge
(ignore tipping). While in the city fares with probability 2/3 want a short trip
that lasts an amount of time uniformly distributed on [2, 10] minutes and the
cab driver earns an average of $1.33 a minute (i.e., 4/3 of a dollar). (a) In the
long run how much money does he make per hour? (b) What fraction of time
does he spend going to and from the airport (inducing the time spent in line
there)?
A Philadelphia taxi driver gets new customers at rate 1/5 per minute.
With probability 1/3 the person wants to go to the airport, a 20 minute trip.
After waiting in a line of cabs at the airport for an average of 35 minutes,
he gets another fare and spends 20 minutes driving back to drop that person
off. Each trip to or from the airport costs the customer a standard $28 charge
(ignore tipping). While in the city fares with probability 2/3 want a short trip
that lasts an amount of time uniformly distributed on [2, 10] minutes and the
cab driver earns an average of $1.33 a minute (i.e., 4/3 of a dollar). (a) In the
long run how much money does he make per hour? (b) What fraction of time
does he spend going to and from the airport (inducing the time spent in line
there)?
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