ISyE 6650
Probabilistic Models
Fall 2007
Homework 3 Solution
1. (Ross 3.5)
(a) P cfw_X = i|Y = 3 = P cfw_i white balls selected when choosing 3 balls
from 3 white and 6 red
3
i
=
6
3i
9
3
, i = 0, 1, 2, 3.
(b) By same reasoning as in (a), if Y = 1, then
ISyE 6650
Probabilistic Models
Fall 2007
Homework 4 Solution
1. (Ross 4.3)
In this case, the state of the system is determined by the weather conditions in the last three days. Letting D indicate a dry day and R indicate
a rainy day, the possible weather
ISyE 6650
Probabilistic Models
Fall 2007
Homework 5 Solution
1. (Ross 5.3)
Due to the memoryless property of the exponential distribution, the conditional distribution of X , given that X > 1, is the same as the unconditional
distribution of 1 + X . Hence
ISyE 6650
Probabilistic Models
Fall 2007
Homework 1 Solution
September 26, 2007
1. (Ross 1.3)
S = cfw_(e1 , e2 , , en ), n 2 where ei cfw_heads, tails
In addition en = en1 = heads and for i = 1,.,n-2 if ei = heads, then
ei+1 = tails.
Pr cfw_4 tosses = Pr
ISyE 6650
Probabilistic Models
Fall 2007
Homework 2 Solution
1. (Ross 2.1)
A characterization of the sample space of this experiment can be naturally
obtained as follows: First, we assign some sort of i.d. to each of the 10 balls
in the urn, for instance,