ENGRD2700
Basic Engineering Probability and Statistics
Spring 2009
Homework 3: Conditional Probability, Independence, Discrete Random Variables.
Hand in by 1:30 pm on Friday, February 13 in the ENGRD2700 dropbox.
Be sure to write your name and section number (1–6) on your homework.
Make sure that your homework pages are
stapled
together. This homework has 10 parts.
NOTE:
Your answers will, as always, be graded on the clarity of your writing as well as the correctness
of the answer. You must show your work to receive full credit.
1. Disjointness and Independence
Roll two dice and let
A
= ”the first die is 4”. Let
B
1
= ”the second die is 2”. Assume equal likelihood
for each of the six sides on each die. Intuitively the outcome of the first has nothing to do with the
outcome of the second.
(a) Check whether the events
A
and
B
1
are independent.
(b) Let
B
2
= ”the sum of the two dice is 3”. Are the events
A
and
B
2
disjoint? Why?
(c) Are the events
A
and
B
2
independent? Why?
(d) Let
B
3
= ”the sum of the two dice is 9”. Are the events
A
and
B
3
disjoint? Why?
(e) Are the events
A
and
B
3
independent? Why?
(f) Let
B
4
= ”the sum of the two dice is 7”. Are the events
A
and
B
4
disjoint? Why?
(g) Are the events
A
and
B
4
independent? Why?
(h) Briefly state some conclusions you have drawn from this question.
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.
 Spring '05
 STAFF
 Probability, DeVore

Click to edit the document details