1.

A player is to throw a die, and, if the face with an even number of spots shows up, the player wins the prize. What is the probability of winning the prize? Formulate the problem and solve it using the axiomatic approach.

2.

The number of switched virtual circuit requests arriving at an ATM switch during the period of from 9:00 a.m. to 10:00 a.m. has been counted over 30 days. The total count is 900 requests. What is the arrival rate during the 9:00 10:00 a.m. period?

3.

ATM cells arrive at an ATM switch at the rate of ? = 600 cells/minute. Assuming that the arrivals are Poisson, what is the probability that two cells will arrive in a 0.1-second interval? (Use the Poisson distribution; use e ? 2.72; e ^-1 ? 0.37.)

4.

Packets arrive at a packet switch at the rate of 10x10 ⁶ packets/sec from 8:00 a. m. to 9:00 a.m. and 5xl0 ⁶ packets/sec from 9:00 a.m. to 10:00 a.m. Would it be reasonable to assume that the arrival pattern over the 8:00 a.m. 10 a.m. period is Poisson and why?

5.

Is the following statement true or false?

• An arrival pattern of passengers at a train station over a certain period has been found to be non-stationary and ergodic.

• A Poisson process is stationary and ergodic.

6.

A packet switch has...