Review
Section 2.7: Independent Events
Example 8: When you flip a thumbtack, it can land
either point up (with probability 0.32) or point down
(with probability 0.68). When we flip five times,
what is the chance that it lands point down on all
five flips?
Stat 4201 Introduction to Mathematical Statistics I
Autumn Semester 2012
Lecture: MWF 9:10-10:05 AM in Evans Lab 1008
Instructor: Dennis Pearl
Office: 440F Cockins Hall
Phone: 292-3887
Office Hours: TW 10:20 am or by appointment
Email: Pearl.1@osu.edu
TA:
Statistics 4201
Homework #4
Autumn 2012
Due in lecture on Friday, September 21, 2012
Note: You might want to scan or copy your solutions before submitting them since you will
not receive your assignment back before the rst exam.
1. (3 points) Chapter 4, E
Statistics 4201
Homework #2 Solution
Autumn 2012
1. Chapter 2, Exercise 21
Want to Show: If P (B |A) = P (B ) and P (B ) = 0, then P (A|B ) = P (A).
One Possible Proof:
P (A B )
by denition of conditional probability
P (B )
P (B |A) P (A)
=
by theorem bas
Announcement:
Shuang Xia has
changed her office
hours to
Thursday 11-12 and
2-3
Review Section 4.1/4.2: The Expected Value
Example 2: The time, Y (in milliseconds), it takes
for a chemical reaction to complete follows the
probability distribution
f(y) = 5
REVIEW Section 3.5: Multivariate Distributions
Example 5: Water flows into a pond from two
streams that each carry trout and catfish stocked in
upstream lakes. The proportion of water in the
pond from the first stream, X, and the proportion of
the fish (b
Review
Section 4.6: Product Moments
With two or more variables there are other moments
to consider for the joint distribution. For example, for
two variables X and Y, the jth and kth product moment
about the origin is defined by
'
j ,k
jk
= E ( X Y ).
Wh
Section 3.5: Multivariate Distributions
Example 4: A small bed-and-breakfast has 3
rooms for rent including two with king-sized beds
and one with two queen-sized beds. The
probability distribution for the number of rooms, X,
rented on a weekend is given b