## Statistics: how often can something “better” be expected to perform better?

Tutoring statistics, you might imagine everyday situations. The tutor brings up one. Let’s imagine we have two mile runners. Runner 1, called R1, has mean time 4:45, with standard deviation 10s; R2 has mean time 5:00 with standard deviation 12s. …

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## Probability: when to add, when to multiply

The tutor offers points about combining probabilities. My gut reaction, thinking about when to add probabilities, is that it’s done less often than multiplying. However, there is one obvious type of situation in which you add: Example 1 Each ticket …

## Math: conditional probability: a first example

The tutor wades into a case of conditional probability. Conditional probability involves the idea that with extra knowledge of a situation, the likelihood of a given outcome can change. Consider the following premise: Example 1 At ABC Insurance, the general …

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## Math: probability: unequal likelihood and odds

The tutor imagines an experiment in probability. For most people, probability becomes interesting when you can apply it to a believable situation. Let’s explore the following premise: Example 1 Around a farm live twelve wild foxes. Eleven are red, but …

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## Perl random walk simulation: code explanation

The tutor continues with some explanation of last post’s Perl random walk simulation. Below is the Perl code from last post, this time with some comments (recall that # denotes a comment in Perl): #!/usr/bin/perl # needed for Linux (Unix) …

## Probability: Markov chains: introduction

The tutor is happy to introduce the elegant topic of Markov chains. A Markov chain is a sequence of states through which a probability system can pass. It’s not so complex as it sounds. Consider the following example: Ms A …