Question

PLEASE SHOW WORKING

A passenger is on a plane with one stop in Chicago. The arrival time of airplane in Chicago is a random variable X with a uniform distribution between 40-50 minutes. The connecting flight will depart from Chicago in one hour. The time for the passenger to get off the plane and then run the connecting flight before its door is closed will be another random variable Y with a uniform distribution between 12 minutes to 22 minutes.DO

a) are X AND Y INDEPENDENT OR NOT AND WHY?

B) Find the marginal probability distribution function of X and the marginal probability distribution function of Y

C) Give the joint probability distribution function of X and Y (HINT: since both X and Y have uniform distribution, the joint probability distribution must be constant k)

D) What the probability that the plane arrives in less than 45 minutes? What’s the probability that the passenger needs more than 15 minutes to get to the gate of the connecting flight?

E) what the probability that the passenger can catch up the connecting flight?

F) E(X)=? And E(Y)=?, COV(X,Y)=?

Answer 1

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