1 (due to 1/29)   Ch 1. 3, 4,  8, 11, 19.

2. (due to 1/31) Ch 1. 26, 30, 36, 37, 45.

3. due to 2/4) Ch 2. 4, (i) and (ii), 5 (i) and (ii), 12, 33, 40 ( only find distribution)

4. (due to 2/7 Ch 2. 48, 50, 63.

5 (due to 2/12) Ch 2. 68 (ii), Ch 4. 3.

6. (due to 2/14) Ch 4: 2, 6, 8, 10 .

7. (due to 2/19) Ch 4.  14,  17.

8. (due to 2/21) Ch 4: 23, 29, 33, 34 (assume that p_i=1/2 for i=1,2,3), 56.

9. (due to 2/28) Ch 4: 66 amd two extra problems.

(a) One does a simple ranom walk on the following graph. Fins the hitting probability reaching to a before b.

            b   b

     a     c    d  b

     b     e    f   b

            b    b

(b)  A rat is put into a maze. Suppose that the rat walks randomly on these following numebrs. What it the probability that the rat find the food before the shock?

           1     2    3(food)

           4     5     6

           7(shock)

10. (due to 3/18) Ch 5: 1, 2, 4, 5, 6.

11. (due to 4/1) Ch 5: 16, 22 and two extrra problems

1.  Suppose that calls are arriving at a rate of one per second according to a Poisson process. Find

(a) the probability that the fourth call after time t=0 arrives within 2 secs of the third call.

(b) the probability that the fourth call arrives by time t=5 .

(c) the expected time at which the fourth call arrives.

2. AGeiger counter is recording  background radiation at a rate of one hit per minute. Let T(3) be the time in mins when the third hit occurs after counter is swiched on.

Find the probability that T(3) is betewwn 2 and 4 (mins) .

12. ( due to 4/3) Ch 5: 20, 37, 39, 42 (a), (c), 44

13. (due to 4/10) Ch 6:  13, 15, 17, 23

14: (due to 4/22) Ch 8: 8, 11, 15, 16, 20. Extra:  Cars come to a garage with rate 3/week and the fix rate for the garage is 2/week. The garage allows only N cars inside.

Each car costs $100/week. The garage pay $500 to fix each car outside. When N=2, 3,4, totoal cost is $837 and $ 820 and $852, respectively. You need to check the cost when N=5,6.

15: (due to 4/29) Ch 9: 2, 5, 8,11, 14

16: (due to 5/2)                         ---------0.3----0.4 ---0.3---

                                           ----|                                           |------ Find the expected life time of the system (the number in the graph are rates).

                                                 -------0.1------0.1----------