M 362K, Spring 03, Smith

## Assignment for Monday, September 22

I. Read Section 3.4 through Example 4g (p. 87).
• You may  omit part (c) of Example 4f.
• The capital "pi" in Example 87 means take the product of the factors (1 - pi
II. Practice problems:

1. a. Give an example of two events that are independent but not mutually exclusive.
b. Give an example of two events that are mutually exclusive but not independent.
c. What can you conclude if two events are both independent and mutually exclusive?

2. p. 109, #50

3. In a certain parallel system consisting of n components (see Example 4g for what this means), each component independently works with probability p. Let F be the event "the system functions." For i = 1, 2, ..., n, let Ci be the event "the ith component functions."
a. Describe F in terms of C1, C2, ... Cn.
b. Describe Fc in terms of C1, C2, ... Cn.
c. Find P(F).
d. Express F C1 as simply as possible. [Hint: What is the intersection of F and the complement of C1?]
e. What is P(F| C1)?
f. Find P( C1|F).

4. p. 109, #51