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1 Key Terms for Lower Division

1 Introduction to Probability

2 Fundamental Results

3 Conditional Probability

4 Bayes' Rule

5 Independent Events

6 Conditional Probability Function \(P(\cdot|F)\)

7 Random Variables

8 Independent Random Variables

9 Functions of Independent Random Variables

10 Discrete Random Variables and pmf

11 Expectated Value of Discrete Random Variables

12 Standard Deviation and Variance of Discrete Random Variables

13 Properties of Variance

14 Bernoulli, Binomial, and Geometric Distributions

15 Poisson Distribution

16 Continuous Random Variables

17 Cumulative Distributions Functions (cdf)

18 Joint Distributions

19 Conditioning on Continuous Random Variables

20 Independent Continuous Random Variables

21 Order Statistics

22 Expected Value of Continuous Random Variables

23 Continuous Uniform and Exponential Distributions

24 Normal Distribution

25 Median and Percentiles

26 Covariance and Correlation

27 Variance of Sums of Random Variables

28 Conditional Expectation

29 Sums of Independent Random Variables

30 Moments and Moment Generating Functions

31 Strong Law of Large Numbers

32 Central Limit Theorem

1 Definition of a Probability Measure