6280: Performance Evaluation of Communication Networks


HW 2:  Due September 16, 2003  in class



PRACTICE PROBLEMS


Chapter 2 problems


27, 38, 47, 68

Chapter 3 problems

13, 23, 37

Problem A:

  An airplane used for any particular flight on COmputing Airlines has a 
capacity of n passengers where n is a discrete random variable with 
z-Transform

  F(z) = 2 A [ 0.5 z^6 + 0.3 z^7 + 0.2 z^8] ^5

a)Determine the value of $A$.
b) What is the expected value of the capacity of a plane picked at
random.
c) What are the capacities of the smallest and largest planes.


Problem B

Wisgets are packed into cartons which are packed into crates. 

The weight, X, (in pounds) of a widget is a continuous random variable 
with an exponential distribution and mean 1/lambda.

The number of widgets in any carton, K, is a random varible with a
Poisson PMF and mean 1/mu

The number of cartons in a crate, N, is a random variable with a 
Geometric distribution with mean 1/P

RVs X, K, and N are mutually independent.

Determine:

a) The probability that a randomly selected crate contains exactly 
one widget.

b) The conditional pdf for the total weight of widgets in a carton
given that teh carton contains less than two widgets.

c) The laplace transform of the pdf for the total weight of widgets 
in a crate.

d) The probability that a randomly chosen crate contains an
odd number of widgets.



  HAND IN PROBLEMS


Chapter 2:  43,

Chapter 3:  74