Download Study Guide - Probability

Probability
Study Guide for Section 6.8
Note: We are only covering basic probability distributions and the normal distribution. You do not
need to worry about average values or the exponential distribution.
1. Random Variables and Probability Distributions
A random variable is any measurement whose value includes an element of randomness. Any
random variable \ has a probability distribution (or probability density function) 0 aBb that
represents the relative likelihood of different values for \ . For example, the following
distribution shows a random variable that takes on values between " and &, with values between
" and $ being much more likely than values between $ and &:
C
B
1
2
3
4
5
6
You can find the probability that \ lies in a certain range by finding the area in that range under
the graph of 0 aBb:
,
T a+ Ÿ \ Ÿ ,b œ ( 0 aBb .B
+
Note that the total area under a probability distribution must be ".
Problems: 3, 8
2. Normal Distributions
The most common kind of probability distribution is the normal distribution (or bell curve):
5
5
.
The central (or average) value of the distribution is called the mean, and is denoted by the Greek
letter . (mu). The “width” of the distribution is called the standard deviation, and is denoted
by the Greek letter 5 (sigma). The formula for a normal distribution with mean . and standard
deviation 5 is:
0 aBb œ
#
"
"
#
/ # aB.b Î5
5 È #1
The simlest case is when . œ ! and 5 œ ". This is called the standard normal distribution:
0 aBb œ
Problems: 13, 15, 17
" #
"
/ # B
È #1