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 - p
_{i})

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 C_{i}
be the event "the ith component functions."

a. Describe F in terms of C_{1}, C_{2},
... C_{n}.

b. Describe F^{c} in terms of C_{1},
C_{2}, ... C_{n}.

c. Find P(F).

d. Express F C_{1} as simply as possible. [Hint:
What is the intersection of F and the complement of C_{1}?]

e. What is P(F| C_{1})?

f. Find P( C_{1}|F).

4. p. 109, #51