Question:

Suppose there are two afternoon flights from New York to Chicago. The arrival time of Flight A is a random variable Ta which is uniformly distributed on the interval (1:00pm, 1:20pm). The arrival time of Flight B is a random variable Tb which is uniformly distributed on the interval (1:10pm, 1:30pm). Suppose that Ta and Tb are independent.

1. Compute P (Ta
2. Given that neither flight arrives before 1:15pm, what is the probability that Flight A arrives first?
3. If T* = min(Ta, Tb) is the time of the first arrival, find the density for T* on R .
4. Compute E(T*).

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