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:
X_{1}, X_{2}, ... , X_{n} are independent,
identically distributed random variables with mean µ_{1} and
standard deviation sigma_{1}. Also, Y_{1}, Y_{2},
... , Y_{m} are independent, identically distributed random variables
with mean µ_{2} and standard deviation sigma_{2}.
The Y's are also independent of the X's. We need to study the new random
variables

X-bar = (1/n)(X_{1}+ X_{2}+ ... ,+X_{n})
and Y-bar = (1/m)(Y_{1}+ Y_{2}+
... ,+Y_{m})

(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.)