M 362K, Spring 03, Smith
Assignment for Monday, December 1
I. Read Section 7.3 through the top of p. 332.
II. Practice problems:
1. p. 383 #31
2. p. 383 #37
3. Situations such as the following often arise in statistics:
X1, X2, ... , Xn are independent,
identically distributed random variables with mean µ1 and
standard deviation sigma1. Also, Y1, Y2,
... , Ym are independent, identically distributed random variables
with mean µ2 and standard deviation sigma2.
The Y's are also independent of the X's. We need to study the new random
variables
X-bar = (1/n)(X1+ X2+ ... ,+Xn)
and Y-bar = (1/m)(Y1+ Y2+
... ,+Ym)
(They are the respective averages of the X's and the Y's.)
Find:
a. The mean and standard deviation of X-bar
b. The mean and standard deviation of Y-bar
c. The mean and standard deviation of (X-bar) - (Y-bar).
[Useful fact: Since the X's and Y's are all independent, it follows that
X-bar and Y-bar are independent.)