Autumn Semester 2016
July 30, 2016
IE 611: Introduction to Stochastic Models
Practice Problems
Exercise 1 Consider two boxes, one containing one black and one white marble, the other,
two black and one white marble. A box is selected at random and a marbl

Autumn Semester 2016
August 17, 2016
IE 611: Introduction to Stochastic Models
Tutorial 4
Exercise 1 Solve all questions of quiz-1.
Exercise 2 Three white and three black balls are distributed in two urns in such a way that
each contains three balls. We s

Autumn Semester 2016
August 3, 2016
IE 611: Introduction to Stochastic Models
Tutorial 3
Exercise 1 Let X be the continuous random variable with pdf fX (x); Find E[X|X > 1].
Exercise 2 Random variables X and Y are distributed according to the joint PDF
(

Autumn Semester 2016
July 26, 2016
IE 611: Introduction to Stochastic Models
Tutorial 1
Exercise 1 Let E F show that P (E) P (F ).
Exercise 2 Let A and B be two events. Use the axioms of probability to prove the following:
(a) P (A B) P (A) + P (B) 1.
(b)

Autumn Semester 2016
July 18, 2016
IE 611: Introduction to Stochastic Models
Tutorial 0
Sample space
Exercise 1 Consider the following experiments and write the sample space.
Experiment consist of flipping one/two coin.
Rolling one/two die.
Exercise 2 A

Autumn Semester 2016
August 31, 2016
IE 611: Introduction to Stochastic Models
Tutorial 6
Exercise 1 Specify the classes of the following Markov chains, and determine whether they
are transient or recurrent:
Exercise 2 Consider a Markov chain whose transi

Autumn Semester 2016
August 24, 2016
IE 611: Introduction to Stochastic Models
Tutorial 5
Exercise 1 Three white and three black balls are distributed in two urns in such a way that
each contains three balls. We say that the system is in state i, i = 0, 1

Autumn Semester 2016
August 3, 2016
IE 611: Introduction to Stochastic Models
Tutorial 2
Exercise 1 Conditional Probability
(a) At a party N men throw their hats into the center of a room. The hats are mixed up and
each man randomly selects one. Find the