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Problem 3. Alice is waiting for a bus at a bus stop. She needs to take...

Problem 3. Alice is waiting for a bus at a bus stop. She needs to take a bus number 10 or 12, and she takes the first suitable bus that arrives. The arrival time of bus 10 is exponential with λ10 = 6/19, and the arrival time of bust 12 is exponential with λ12 = 3/19. Moreover, arrival times of 10 and 12 are independent.

  • What is the probability that Alice will take bus number 10 instead of bus number 12?
  • Let X be amount of time Alice has to wait. Find PDF of X.
  • What is P (X > 1)?
  • How long on average Alice has to wait for any bus to arrive?
Math   Statistics-And-Probability   
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hii..if you have any doubt please ask by comment. thanks..

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