Question: After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening". Assume that this means that the time T of the call is uniformly distributed in the specified interval. Assume that you know in advance that the call will last exactly $1$ hour. From $9$ to $9:30$, there is a game show on $TV$ that you wanted to watch. Let $M$ be the amount of time of the show that you miss because of the call. Compute the expected value of $M$.
What I have understood is $P(M | X < 8:00) = 0$, i.e. probability that show will be missed is $0$ when call is received before $8:00$. If I consider time b/w $8:00$ to $8:30$, then expected value is $(8:30-8:00)/2 = 15.$ Is it the right way to proceed. I don't know what is actual answer.