The state of a particular continuous time Markov chain is defined as the number of jobs currently at a certain work center, where a maximum of two jobs are allowed. Jobs arrive individually. Whenever fewer than two jobs are present, the time until the next arrival has an exponential distribution with a mean of 2 days. Jobs are processed at the work center one at a time and then leave immediately. Processing times have an exponential distribution with a mean of 1 day.
(a) Construct the rate diagram for this Markov chain.
(b) Write the steady-state equations.
(c) Solve these equations for the steady-state probabilities.

You have $600,000 saved for retirement. your account earns 5.5% interest. how much, to the nearest dollar, will you be able to pull out each month, if you want to be able to take withdrawals for 20 years?

At the olympic games, many events have several rounds of competition. one of these events is the men's 100-meter backstroke. the upper dot plot shows the times (in seconds) of the top 8 finishers in the final round of the 2012 olympics. the lower dot plot shows the times of the same 8 swimmers, but in the semifinal round. which pieces of information can be gathered from these dot plots? (remember that lower swim times are faster.) choose all answers that apply: a: the swimmers had faster times on average in the final round. b: the times in the final round vary noticeably more than the times in the semifinal round. c: none of the above.

How many terms does the polynomial x^2 y^2 have