In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus If the waiting time (in minutes) at each stop has a uniform distribution with A 0 and B 5, then it can be shown that the total waiting time Y has the pdf a Sketch a graph of the pdf of Y b Verify that curren Ecirc f(y) dy 1 c What is the probability that total waiting time is at most 3 min d What is the probability that total waiting time is at most 8 min e What is the probability that total waiting time is between 3 and 8 min f What is the probability that total waiting time is either less than 2 min or more than 6 min 25 f(y) 2 1 5 25 5sys io 0

Question: In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting

In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform with A = 0 and B = 5, then it can be shown that the total waiting time Y has the pdf

a. Sketch a graph of the pdf of Y.
b. Verify that ‰¤ Êƒˆž-ˆžf(y) dy = 1.
c. What is the probability that total waiting time is at most 3 min?
d. What is the probability that total waiting time is at most 8 min?
e. What is the probability that total waiting time is between 3 and 8 min?
f. What is the probability that total waiting time is either less than 2 min or more than 6 min?

25 f(y)-2 1 5 25 5sys io 0

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