The Union and Intersection for Different Configurations of Two Events Mutually Exclusive vs Independency of Events

Transcription

1 Section 1: Introductory Probability Basic Probability Facts Probabilities of Simple Events Overview of Set Language Venn Diagrams Probabilities of Compound Events Choices of Events The Addition Rule Combinations of Events The Multiplication Rule Dependent Events Conditional Probabilities Independent Events The Union and Intersection for Different Configurations of Two Events Mutually Exclusive vs Independency of Events Probability Diagrams Tree Diagrams Venn Diagrams Karnaugh Maps Section 2: Counting Techniques Factorials Permutations Combinations Section 3: Random Variables and their Distributions Discrete Random Variables Continuous Random Variables Probability Distributions and Functions Discrete Probability Distributions Continuous Probability Distributions The Cumulative Density Function Parameters Used to Describe Probability Functions Measures of Central Tendency The Mean Value (Expected Value) The Median The Mode

2 Measures of Spread The Range The Interquartile Range The Variance and Standard Deviation Shapes of Probability Distributions Section 4: General Discrete Probability Distributions Characteristics of Discrete Probability Distributions Finding Probabilities The Expected Value or Mean Properties of E(X) The Expected Value of a Function The Variance The Variance of Functions The Standard Deviation Two Sigma Property Section 5: The Binomial Distribution Properties of Bernoulli Sequences Using CAS Technology to Find Probabilities in Binomial Distributions The Mean and Standard Deviation of Binomial Distributions Calculating the Trial Size Given a Probability The Binomial Probability Distribution Graph Section 6: Select VCAA Questions Short Answer Questions Multiple Choice Questions Extended Response Questions Section 7: The Continuous Probability Distribution Probabilities of Simple PDFs Probabilities of Complex PDFs The Mean of Simple PDFs The Mean of Complex PDFs The Mean of Functions in Terms of X The Median of Simple PDFs The Median of Complex PDFs The Mode The Variance and Standard Deviation of Simple PDFs The Variance and Standard Deviation of Complex PDFs The Variance of Functions in Terms of X

3 Sums of Independent Variables The Range Percentiles and Quantiles The Interquartile Range VCAA Questions Continuous Distributions Section 8: The Normal Distribution Graphs of the Normal Distribution Finding Probabilities Using Confidence Intervals Finding Probabilities Using Technology The Standard Normal Distribution Calculating Z Values Page Symmetry Properties of the Standard Normal Curve Finding Probabilities from Z Scores The Inverse Normal Distribution Finding the Value of X or Z Given a Probability Finding the Value of a Normal Random Variable VCAA Questions Normal Distribution

4 Important Definitions in Statistics Common Notations Sampling Distribution Statistical Inference Random Sampling Important Definitions What is Sampling? The Sampling Process Non-Probability Sampling A. Judgment Sampling B. Quota Sampling C. Convenience Sampling Probability Sampling D. Simple Random Sampling E. Systematic Random Sampling F. Stratified Random Sampling G. Cluster Sampling Accuracy, Bias, Variability and Precision Errors in Sampling Proportions Sample Proportions Population Proportions Sampling Distribution of the Sample Proportion Sampling from Large Populations Sampling from Small Populations Approximating the Sampling Distribution of the Sample Proportion With the Normal Distribution How to Determine Whether a Sample is Large Properties of the Normal Approximation for the Sampling Distribution of the Sample Proportion Calculating Probabilities Using the Normal Approximation

5 Estimators Point Estimates Confidence Intervals Interpreting Confidence Intervals Confidence Intervals for Population Proportions Confidence Levels Confidence Interval Formulae Critical Values & Multipliers Calculating Critical Values Finding a Confidence Interval for The Margin of Error Calculating the Margin of Error Factors that Affect the Margin of Error Confidence Intervals in Terms of the Margin of Error Factors that Affect the Width of Confidence Intervals Finding the Point Estimate & Margin of Error from a Confidence Interval Calculating the Sample Size Needed to Estimate Certainty vs Precision p p

6 Integration and its Applications Integrating Algebraic Expressions Integrating Expressions General Approach Integrating Integrating Trigonometric Expressions Integrating Exponential Expressions Integrating Integrating ( ax b) 1 x g'( x) gx ( ) Integrating Hybrid Functions Integrating Composite Functions Applications in Integration n Solving for the Constant c Integration by Recognition Definite Integrals Important Properties of the Definite Integral Approximating the Area Under a Curve The Left Endpoint Approximation The Right Endpoint Approximation Using Integration to Find Areas Under Curves Changing the Sign of an Area Calculating Unsigned Areas or Areas Solving for an Unknown Given an Area or Definite Integral Areas Between Curves The Average Value of a Function Graphs of the Antiderivative Function Applications of Calculus to Motion in a Straight Line The Fundamental Theorem of Calculus Revisited