UNIVERSITY OF WATERLOO
DEPARTMENT OF MANAGEMENT SCIENCES
MSCI 431: STOCHASTIC MODELS AND METHODS
WINTER 2023
Practice Set: CH3
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Instructor: Dr. Jim Bookbinder, Jan 29, 2023 by Affleck Chang
The copyright of the questions is
(2014) Sheldon M. Ross - Introduction to Probability Models-Academic Press 11th.
(2019) Sheldon M. Ross - Introduction to Probability Models-Academic Press 12th.
3. E[X|Y=1] = 2, E[X|Y=2] = 5/3, E[X|Y=3] = 12/5 4. No
5. (a)
(b) 5/3
6. (a) P{X=0|Y=3} = 8/27, P{X=1|Y=3} = 4/9, P{X=2|Y=3} = 2/9, P{X=3|Y=3} = 1/27
(b) 5/3
(a) 9/5 (b) 1
(a) 6 (b) 7 (c)
9.
11.
Ans:
Ans:
Ans:
(a) 22/9 (b) 4
No.24 and 27 are challenging, they are similar cases to Ex. 3.15, therefore, please study Ex 3.15 as well.
We do not test it on quizzes usually, but we encourage you to try it. However,
it is possible to test the simple version on Midterm/Final, and it is useful for your project calculation.
24.
27.
37. (a) 3 (b) 3.1067
38.
(a) 9.5 days (b) 2.5 days
(a)
(b)
(a) 6.6 (b)
(c) 15.24