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AMS102.03 Handout 4
Summary of Chapters 6 and 7
Chapter 6
Density Curve: Graphic representation for distribution of a continuous variable
 The total area under the curve is one
 The area under the curve between two values represents the proportion of
observations falling between the two values
Normal Distribution
 Notation: N(μ, σ)
 Tables of Standard Normal distribution N(0,1)
 Transform non-standard to standard normal:
X 
Z

 Use the table to find proportion given values, find values given proportion
 Draw the right curve following 68-95-99.7 rule, helpful for many problems
 Use 68-95-99.7 rule for problems when possible
Spike graph for discrete variables
Hypothesis Testing: Use density curves and spike graph to find P-values and Type I,
Type II error.
Chapter 7
Probability: Frequency of certain outcome in a long run of repetitions.
Sample Space, Basic Outcomes, Events
Probability of Events
 Venn Diagrams are helpful
 A or B (A  B)
 A and B (A  B)
 Addition Rule: P(A or B) = P(A)+P(B)-P(A and B)
 Events A and B are mutually exclusive if they can not happen simultaneously
Conditional Probability of event A when event B had happened, P(A|B)
 Sample space reduced to only cases where B is true
 Use Venn Diagram
 Find conditional probability given contingency tables
Expected Value (Expectation, Mean): E ( X )  x1 p1  x2 p2  ....  xl pl
 Know how to compute given the distribution of discrete variables, i.e. xi and pi.