ORIE 3500/5500 – Engineering Probability and Statistics II
Fall 2010
Assignment 10
Problem 1
As punishment for committing a particularly heinous
crime you have been sentenced to jail under the following terms. Upon
entering jail you draw a ball from a box containing balls numbered 0,
1 and 3 respectively. If you draw the ball numbered 0, you get out of
jail immediately. If you draw 1 or 3, you replace the ball in the box
and stay that many years in jail, at which time you draw again, under
the same conditions. This is repeated until you draw the zero and go
free. How long do you expect to be in jail?
Hint
: condition on the
ﬁrst ball drawn.
Problem 2
A lottery player decides to use a random variable gen
erator to help him decide how many tickets to buy. He generates a
discrete uniform random variable
N
taking values of 1 through 5 with
equal probabilities, and then purchases
N
lottery tickets. If each of the
tickets he buys has (independently of the other tickets) the probability
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '10
 SAMORODNITSKY
 Poisson Distribution, Probability theory, random variable generator, particularly heinous crime, unknown shape parameter, xk e−x dx

Click to edit the document details