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STAT 300 - Modern Probability & Statistics

Beginner

Updated 08/2023

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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.

Prerequisites

There are no prerequisites for this course

2015 Trial

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1

Introduction to R

How this works

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Basic arithmetic with R

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Assigning variables

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What does this do?

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Variable assignment (2)

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Variable assignment (3)

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Apples and oranges

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Basic data types in R

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What's that data type?

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2

Vectors and Data Frames

Create a vector

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Vector operations

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Vector operations (2)

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Vector selection

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Data Frames

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Selecting columns from a data frame

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Creating a new variable

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Select observations within a data frame

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3

Intro to Statistical Inference

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Simulate a coin toss

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Flip a coin multiple times

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What does this do?

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Counting heads (results from our simulation)

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Determining likelihood of our null hypothesis

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What does a p-value represent?

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What can we conclude from a p-value?

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Determining likelihood of our null hypothesis (2)

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Last p-value from the dolphin study

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Your turn: Randomization-based inference

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Interpreting a p-value.

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Sexism in bank promotions

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Replicating the promotion data

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Promotion data p-value estimation

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4

Probability & Counting

Activity #2, Question #5: Running proportion of heads

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Question 7: Probability model for number of heads in 3 tosses

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Question 8: Rolling two dice and getting a sum of 7

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Question 11: Guessing answers to a 10-question true/false quiz.

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Question 14: What's in a name?

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What's in a name? (2)

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What's in a name? (3)

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Question 15: Arranging the letters ABCD

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Sampling with or without replacement.

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Questions 16-25: Combinations and Permutations

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Question 31: Choosing students to fail

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5

Counting & Permutation Tests

Activity #3, Questions #1-4

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Using a simulation approach

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Prediction...

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Questions 8-13: Guessing answers to test questions

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Calculate the probability...

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Questions 14-16: Random babies.

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Your turn: Question #17.

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Questions 18-20: Contagious yawns

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What can we conclude from this p-value?

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Questions 21-28: Does the drug make you faster?

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What can we conclude from this p-value? (2)

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6

Binomial Distribution

Guessing answers to multiple-choice quizzes

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10-question quiz simulation

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Using the binomial distribution

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Dolphins, revisited

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Dolphins, revisited (again)

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Blindfolded pigeons (questions 27-30 in the activity)

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What can we conclude from this p-value?

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Calculate the probability...

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7

Discrete Distributions

Question #1: You are looking for a free agent who can hit .300.

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10-question quiz simulation

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Using the binomial distribution

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Dolphins, revisited

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Dolphins, revisited (again)

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Blindfolded pigeons (questions 27-30 in the activity)

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What can we conclude from this p-value?

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Calculate the probability...

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STAT 300 - Modern Probability & Statistics

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