A tiny router has a queuing capacity to store 10 packets in its buffer. It has to drop any further packets arriving at it when its buffer is full. At every millisecond, the router either: i) sees an arrival with
probability 0:2, ii) completes forwarding of a packet with probability 0:6 (if its buffer is not empty; with
probability 0 otherwise), or iii) stays the same – no new arrival and no forwarding – with probability
0:2 (when the buffer is nonempty) or with probability 0:8 (when the buffer is empty).
Now determine the followings:
(a) The probability that the router has an empty buffer at any given millisecond.
(b) The probability that it has at least seven packets in its buffer at any given millisecond.

Leslie started last week with $1200 in her checking account. during the week, she wrote the checks below. trans typ./ check no. date description of transaction payment/ debit deposit/ credit (+) balance 1,200 00 324 10/6 miller's food market 45.87 45 87 groceries 1,154 13 325 10/7 cyber center computer outlet 218.59 218 59 monitor 935 54 326 10/9 sandy's beauty salon 30.00 30 00 haircut and styling 900 59 deposit 10/10 paycheck 621.33 621 33 1,621 92 evaluate leslie's check register. a. leslie did a good job. everything is correct. b. the final balance is wrong; she did not add everything correctly. c. leslie should have written debit instead of deposit for the transaction type. d. leslie switched the debit and credit columns.