4. The time (in hours) required to repair a machine is an exponentially distributed random variable with parameter 0= 4. What is the conditional probability that a repair takes at least 3 hours, given that its duration exceeds 1 hours?

At a toll-booth on-ramp there is a stochastic arrival distribution. Vehicles are counted in 20-second intervals, and vehicle counts are taken in 120 of these time intervals. Based on data collected, no vehicles arrived in 18 of the 120 count intervals. What is the number of the 120 intervals that 3 cars arrived?

2

The lifetime (in years) of a washing machine from a particular company is an exponential random variable with parameter 1/5 . The company offers to replace any machine which breaks within 6 months.  (a) What proportion of machines do they need to replace. (b) What is the expected time until a customer needs to buy a new machine? (Each time the company replaces a machine which breaks within 6 months, the company agrees to replace the new machine if it breaks within 6 months.)