 
Summary: ISyE 3232 Stochastic Manufacturing and Service Models Spring 2010
H. Ayhan, T. Cheong
Homework 1 Solution
1. (a) Number of arrivals in certain time interval can be modeled as Poisson random variable.
(b) Time between arrivals is best modeled with exponential random variable.
(c) Number of experiments(sniffs) until a success(alert) should be modeled using a Geometric random
variable.
(d) Whether or not the beagle alerts when sniffing the next bag would best be modeled using a
Bernoulli random variable.
(e) Number of successes (alerts) among certain number of experiments(25 sniffs) can be modeled
using a Binomial random variable.
(f) The combined weight of the next 25 bags containing banned substances could best be modeled
using a Normal random variable.
2. Here we are given that E[X] = 4, Var[X] = 100.
E[6  3X] = 6  3E[X] = 6, Var[6  3X] = 9Var[X] = 900
E[(2X  3)/5] = 2
5 E[X]  3
5 = 1, Var[(2X  3)/5] = (2
5 )
2
