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Bob and Alice plan to meet between noon and 1 pm for lunch at the cafeteria....

Bob and Alice plan to meet between noon and 1 pm for lunch at the cafeteria. Bob’s arrival time, denoted by X, measured in minutes after 12 noon, is a uniform random variable between 0 and 60 minutes. The same for Alice’s arrival time, denoted byY.Bob’s and Alice’s arrival times are independent. We are interested in the waiting time W=|X−Y|.

i. What is the probability that W≤10 if X= 15?

ii. What is the probability that W≤10 if X= 5?

iii. What is average waiting time if X=x, where 0≤x≤60?

iv. What is the average waiting time?

Math   Statistics-And-Probability   
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