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Conflicts: 6_STATINFERENCE/Statistical Inference Course Notes.Rmd
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6_STATINFERENCE/Statistical Inference Course Notes.Rmd

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### Conditional Probability
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* let $B$ = an event so that $P(B) > 0$
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* **conditional probability** of an event $A$, given $B$ is defined as the probability that BOTH $A$ and $B$ occurring divided by the probability of $B$ occurring $$P(A\:|\:B) = \frac{P(A \:\cap\: B)}{P(B)}$$
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* if $A$ and $B$ are ***independent***, then $$P(A\:|\:B) = \frac{P(A)P(B)}{P(A)} = P(A)$$
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* let B = an event so that $P(B) > 0$
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* **conditional probability** of an event A, given B is defined as the probability that BOTH A and B occurring divided by the probability of B occurring $$P(A\:|\:B) = \frac{P(A \:\cap\: B)}{P(B)}$$
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* if A and B are ***independent***, then $$P(A\:|\:B) = \frac{P(A)P(B)}{P(B)} = P(A)$$
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* ***example***
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* for die roll, $A = \{1\}$, $B = \{1, 3, 5\}$, then $$P(1~|~Odd) = P(A\:|\:B) = \frac{P(A \cap B)}{P(B)} = \frac{P(A)}{P(B)} = \frac{1/6}{3/6} = \frac{1}{3}$$
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* `dbinom(k, n, p)` = return the probability of getting `k` successes out of `n` trials, given probability of success is `p`
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### Probability Density Function (PDF)
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* evaluates the probability that the **continuous random variable** takes on a specific value
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* always $\ge$ everywhere
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* total area under the must = 1
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* evaluates the probability that the **continuous random variable** takes on a specific value
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* always $\ge$ 0 everywhere
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* total area under curve must = 1
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* **areas under PDFs** correspond to the probabilities for that random variable taking on that range of values (PMF)
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```{r echo = FALSE, fig.width = 2, fig.height = 2, fig.align = 'center'}

8_PREDMACHLEARN/Practical Machine Learning Course Notes HTML.Rmd

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* ***considerations***
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- must be done _without replacement_
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- random sampling with replacement = _bootstrap_
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+ underestimates of the error
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+ can be corrected, but it is complicated ([0.632 Bootstrap](http://www.jstor.org/discover/10.2307/2965703?uid=2&uid=4&sid=21103054448997))
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+ underestimates of the error, since the if we get one right and the sample appears more than once we'll get the other right
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+ can be corrected with the ([0.632 Bootstrap](http://www.jstor.org/discover/10.2307/2965703?uid=2&uid=4&sid=21103054448997)), but it is complicated
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### K-Fold

8_PREDMACHLEARN/Practical Machine Learning Course Notes.Rmd

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* ***considerations***
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- must be done _without replacement_
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- random sampling with replacement = _bootstrap_
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+ underestimates of the error
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+ can be corrected, but it is complicated ([0.632 Bootstrap](http://www.jstor.org/discover/10.2307/2965703?uid=2&uid=4&sid=21103054448997))
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+ underestimates of the error, since the if we get one right and the sample appears more than once we'll get the other right
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+ can be corrected with the ([0.632 Bootstrap](http://www.jstor.org/discover/10.2307/2965703?uid=2&uid=4&sid=21103054448997)), but it is complicated
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### K-Fold

9_DEVDATAPROD/Developing Data Products Course Notes HTML.Rmd

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* advanced HTML can be added directly to the `index.Rmd` file and most of the time it should function correctly
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* interactive element (quiz questions, rCharts, shiny apps) can be embedded into slidify documents ([demos](http://slidify.github.io/dcmeetup/demos/interactive/))
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- quiz elements
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+ `--- &radio` before slide content for multiple choice (make sure quiz is included in widgets)
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+ `##` = signifies title of questions
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+ the question can be type in plain text format
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+ the multiple choice options are listed by number (`1. a`, `2. b`, etc.)
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+ a page like the one below will be generated when processed with slidify
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```Rmd
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--- &radio
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## Question 1
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What is 1 + 1?
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* RStudio format/runs the code when the document is saved
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### Creating Presentation
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* file --> New File --> R Presentation (`alt` + `f` + `p`)
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* file --> New File --> R Presentation (`alt-f` + `f` + `p`)
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* `class: classname` = specify slide-specific control from CSS
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* `css: file.css` = can be used to import an external CSS file
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- alternatively, a css file that has the same name as the presentation will be automatically loaded

9_DEVDATAPROD/Developing Data Products Course Notes.Rmd

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* advanced HTML can be added directly to the `index.Rmd` file and most of the time it should function correctly
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* interactive element (quiz questions, rCharts, shiny apps) can be embedded into slidify documents ([demos](http://slidify.github.io/dcmeetup/demos/interactive/))
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- quiz elements
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+ `--- &radio` before slide content for multiple choice (make sure quiz is included in widgets)
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+ `##` = signifies title of questions
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+ the question can be type in plain text format
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+ the multiple choice options are listed by number (`1. a`, `2. b`, etc.)
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+ a page like the one below will be generated when processed with slidify
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```Rmd
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--- &radio
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## Question 1
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* RStudio format/runs the code when the document is saved
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### Creating Presentation
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* file --> New File --> R Presentation (`alt` + `f` + `p`)
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* file --> New File --> R Presentation (`alt-f` + `f` + `p`)
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* `class: classname` = specify slide-specific control from CSS
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* `css: file.css` = can be used to import an external CSS file
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- alternatively, a css file that has the same name as the presentation will be automatically loaded

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