ieginning at 12:00 noon. Eighty percent of the vehicles are cars, while the rema

Question

ieginning at 12:00 noon. Eighty percent of the vehicles are cars, while the remainders are trucks, buses, etc. Vehicles arrive at a toll booth on the freeway at the average rate of S/minute in a completely random fashion. The vehicles are counted and arrival times are recorded, larning: some distributions may apply in more than one case, while others not at all 1. # of vehicles until the second non-car. /a/lv/ 2. an indicator Xn, which is 1 if the n vehicle is a car, 0 otherwise. 3. #Of vehicles until the first non-car. Geometer 4. time of arrival of first vehicle epenste 5, time of arrival of vehicle #2 Er/ 6. time between arrival of vehicle #1 and vehicle 412 t '/ 7. number of vehicles arriving during the first 5 minutes Po:ss 8. the number of cars among the first 10 vehicles to arriveho out Inswer the following question 9. Plexactly 5 vehicles arrive during the first minute) 10.P(the first non-car is vehicle #5) nt,'y' : P{the second non-car is vehicle 11. 12. P(two ofthe first ten vehicles are cars}"? Tt#-dle 13. Pthe first vehicle arrives during the first /'s minute? 14. Pthe fifth vehicle arrives during the first minute? 15. P { vehicle #5 is not a car)"? ·( /^%, aih/rwrnd (

Explanation / Answer

Answer:

1. Pascal distribution

2. Bernoulli distribution

3. Geometric distribution

4.Exponential distribution

5. Erlang distribution

6. Exponential distribution

7. Poisson distribution

8. Binomial distribution

9. Poisson distribution

10. Geometric distribution

11. Pascal distribution

12. Binomial distribution

13. Exponential distribution

14. Erlang distribution

15. Bernoulli distribution

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