Math 32 - m32slides

35: Introduction to Machine Learning (2)

Goal: overview of some machine learning techniques

Derek Sollberger

34: Introduction to Machine Learning

Goal: introduce machine learning (ideas and terminology)

Derek Sollberger

Confidence Intervals

Among pennies in circulation in 2019, what was the average year of minting? We have a sample size of 50 pennies.

Derek Sollberger

30: Regression Analysis

Goal: Discuss the validity of regression models

Derek Sollberger

29: Linear Regression

Goal: Summarize bivariate data

Derek Sollberger

28: Beta Distribution

Goal: Explore a distribution of proportions

Derek Sollberger

27: Maximum Likelihood

Goal: Modify distribution parameters based on observed data

Derek Sollberger

26: Likelihood

Derek Sollberger

25: Central Limit Theorem

Goal: Consolidate our understanding of variance

Derek Sollberger

24: Estimators

Goal: Explore generalization from samples to populations

Derek Sollberger

23: Law of Large Numbers

Goal: start to understand error as it relates to sample size

Derek Sollberger

22: Poisson Process

Goal: Derive distribution of number of arrivals

Derek Sollberger

21: Change of Variables

Let \(F\) be the…

Derek Sollberger

20: Correlation

We will once again visualize the act of ordering food at In-n-Out.

Derek Sollberger

19: Covariance

We will once again visualize the act of ordering food at In-n-Out.

Derek Sollberger

18: Linear Operators

Derek Sollberger

17: Continuous Joint Distributions

The joint probability density function \(f(x,y)\) to handle simultaneous calculations of random variables \(X\) and \(Y\) can be expressed as

Derek Sollberger

16: Discrete Joint Distributions

The joint probability mass function (joint PMF) to handle simultaneous calculations of random variables \(X\) and \(Y\) can be expressed as

Derek Sollberger

15: Normal Distribution

Let us start with the mother function \(y = e^{-x^{2}}\)

Derek Sollberger

14: Exponential Distribution

The inclusive versus exclusive variation in inequalities matter in discrete probability distributions. With a random variable \(X\) defined over a support of \(k =…

Derek Sollberger

13: Continuous Distributions

You arrive at a bus stop at 10 o’clock, knowing that the bus will arrive at some time uniformly distributed between 10:00 and 10:30.

Derek Sollberger

12: Geometric Distribution

Here let us assume an endless box of chocolates with random selection with replacement of

Derek Sollberger

11: Cumulative Computation

Last time, we developed the probability mass function for the binomial distribution. The probability of choosing \(k\) observations among a sample size of \(n\), each observation with…

Derek Sollberger

10: Binomial Distribution

To continue our exploration of discrete distributions, we will look at situations that have two disjoint possibilities.

Derek Sollberger

09: Expectation

Suppose that all of the students in Math 32 are between ages 19 and 21 inclusively with the following distribution:

Derek Sollberger

08: Variance

\[s^{2} = \displaystyle\frac{1}{n-1}\displaystyle\sum_{i = 1}^{n} (x_{i} - \bar{x})^{2}\]

Derek Sollberger

07: Measures of Centrality

The Fibonnaci Sequence \(\{1, 1, 2, 3, 5, 8, 13, ...\}\) is an example of a sequence where

Derek Sollberger

6: Bayes’ Rule (Examples)

In 2002, Paul Graham used Bayes’ Rule as part of his algorithms to greatly decrease false positive rates of unwanted e-mails (“spam”). Let \(H^{c}\) be the event…

Derek Sollberger

5: Bayes’ Rule (Concepts)

In the previous section, we studied conditional probability \[P(B|A) = \displaystyle\frac{P(A \text{ and } B)}{P(A)}\] and we talked about how the inverse probabilities \(P…

Derek Sollberger

4: Conditional Probability

Goal: Start to consider dependence in probability

Derek Sollberger

03_-_Complements

Unless otherwise noted, the coin flip has two disjoint outcomes—heads or tails—with probabilities

Derek Sollberger

2: Inclusion-Exclusion

In order to introduce probability concepts, you will notice that many sections of this…

Derek Sollberger

Introduction

Lecturer: Derek Sollberger

Derek Sollberger

Case Study: Yawning

Hypothesis Testing

Derek Sollberger