the time a machine takes to warm up is uniformly distributed

the time a machine takes to warm up is uniformly distributed between 1 and 2 minutes. Once it is warmed up the additional time it takes to run a process is uniformly distributed between 1 and 10 minutes.

a. Including warm up time what is the expected amount of time to run a process on the machine?

b. What is the probability that the machine is warmed up to be exactly 1.5 minutes?

c. What is the probability that the machine is warmed up in less than 1.5 minutes?

d. What is the probability just the processing time is between 4 and 8 minutes?

Solution