Discrete Mathematics for Computer Science

542 CHAPTER 8 Discrete Probability

THEOREMS

Bayes' Rule

Total Probability

8.7 Summary

TERMS

binomial distribution function

binomially distributed hypergeometric distribution

constant random variable h(k; n, r, m)

discrete random variable mean

distribution AI

expectation random variable

expected value

THEOREMS

Basic Property of Expectation Probability Density Defined by a Random

Linearity of Expectation Variable

8.9 Summary

TERMS

independent random variables or

independent, identically distributed standard deviation

(i.i.d.) random variables variance

THEOREMS

Bound on the Probability of Deviation Properties of Variance

from the Expected Value Variance of the Sum of Independent

Expectation of the Product of Independent Random Variables

Random Variables

Law of Averages, or the Weak Law of

Large Numbers

8.11.2 Starting to Review

1. What is a sample space? An outcome? An event?


2. What conditions must a function on a sample space satisfy to be a probability den-
   sity function? What is the difference between the probability of an outcome and the
   probability of an event?


3. What condition on a probability density function p on the sample space QŽ makes p
   a uniform probability density function? Define a uniform probability density function
   on the possible results of rolling a fair die. Compute the probability that the top face
   after the roll of a fair die shows more than four spots, an even number of spots, and
   either one or five spots.


4. List the probability of each outcome in the cross product sample space formed from
   the sample space for flipping a fair coin and the sample space for choosing a number
   from the set {1, 2, 3, 4). For each sample space, use a uniform probability density
   function.