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 density 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.