In a factory, a certain machine operates for a period which is exponentially distributed with parameter . Then it breaks down and will be in repair shop for a period, which is also exponentially distributed with mean 1/. The operating and the repair times are independent. For this machine, we say that a change of state occurs each time that it breaks down, or each time that it is fixed. In a time interval of length t, find the probability mass function of the number of times a change of state occurs.

Lecture 9/25/2017 → Chapter 3: Probability ← SECTION 3.1 Probability: A number between 0 and 1 representing how likely it is that an event will occur. Random Experiment: An experiment whose outcome is not known until it is observed. Sample Space (S): a set of outcomes of a random experiment. Every possible outcome must be listed once and only once. Sample Point:...