A bus holdingeight passengers. After the opening of sales of the tickets, thetim

Question

A bus holdingeight passengers. After the opening of sales of the tickets, thetime (in minutes)between the sales of tickets for the trip has thegamma distribution with 4 and 2 minutes.

Assuming independence, find the probability of being sold outwithin 50 minutes A bus holdingeight passengers. After the opening of sales of the tickets, thetime (in minutes)between the sales of tickets for the trip has thegamma distribution with 4 and 2 minutes.

Assuming independence, find the probability of being sold outwithin 50 minutes

Explanation / Answer

Let T be the time between ticket sells. Given T is gammawith parameters =4 and =2. Then letting=v/2 T will chi-square with parameter and v degrees offreedom. Thus v=2(4)=8 Let the time to sell out all tickets be Y=T1+T2+...+T8 Then Y will be chi-square with v=8+8...+8=64 degrees offreedom Hence P(Y<50)=1

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