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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.