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## Course Description

A Calculus-based introduction to probability and the application of mathematical principles to the collection, analysis, and presentation of data. Modern probability concepts, discrete/ continuous models, and applications; estimation and statistical inference through modern parametric, nonparametric, and simulation/randomization methods; maximum likelihood; Bayesian methods. This course prepares students for the preliminary P/1 exam of the Society of Actuaries and Casualty Actuarial Society.

- 1
### Introduction to R

**Free**In this lab, you'll learn the basics of R. You'll use R as a calculator and then assign some variables.

- 2
### Vectors and Data Frames

**Free**In this lab, you'll learn how to create and access vectors and data frames in R.

- 3
### Intro to Statistical Inference

**Free**After completing this chapter, you'll be able to simulate simple experiments to estimate and interpret p-values.

Load the0 xpSimulate a coin toss0 xpFlip a coin multiple times0 xpWhat does this do?0 xpCounting heads (results from our simulation)0 xpDetermining likelihood of our null hypothesis0 xpWhat does a p-value represent?0 xpWhat can we conclude from a p-value?0 xpDetermining likelihood of our null hypothesis (2)0 xpLast p-value from the dolphin study0 xpYour turn: Randomization-based inference0 xpInterpreting a p-value.0 xpSexism in bank promotions0 xpReplicating the promotion data0 xpPromotion data p-value estimation0 xp - 4
### Probability & Counting

**Free**After completing this chapter, you'll be able to simulate simple experiments to estimate probabilities.

Activity #2, Question #5: Running proportion of heads0 xpQuestion 7: Probability model for number of heads in 3 tosses0 xpQuestion 8: Rolling two dice and getting a sum of 70 xpQuestion 11: Guessing answers to a 10-question true/false quiz.0 xpQuestion 14: What's in a name?0 xpWhat's in a name? (2)0 xpWhat's in a name? (3)0 xpQuestion 15: Arranging the letters ABCD0 xpSampling with or without replacement.0 xpQuestions 16-25: Combinations and Permutations0 xpQuestion 31: Choosing students to fail0 xp - 5
### Counting & Permutation Tests

**Free**After completing this chapter, you'll be able to apply counting rules to estimate likelihoods.

Activity #3, Questions #1-40 xpUsing a simulation approach0 xpPrediction...0 xpQuestions 8-13: Guessing answers to test questions0 xpCalculate the probability...0 xpQuestions 14-16: Random babies.0 xpYour turn: Question #17.0 xpQuestions 18-20: Contagious yawns0 xpWhat can we conclude from this p-value?0 xpQuestions 21-28: Does the drug make you faster?0 xpWhat can we conclude from this p-value? (2)0 xp - 6
### Binomial Distribution

**Free**After completing this chapter, you'll be able to calculate probabilities under the Binomial Distribution.

- 7
### Discrete Distributions

**Free**After completing this chapter, you'll be able to calculate probabilities under the Binomial Distribution.

Question #1: You are looking for a free agent who can hit .300.0 xp10-question quiz simulation0 xpUsing the binomial distribution0 xpDolphins, revisited0 xpDolphins, revisited (again)0 xpBlindfolded pigeons (questions 27-30 in the activity)0 xpWhat can we conclude from this p-value?0 xpCalculate the probability...0 xp

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