ma206distributions and ma206equations

class: inverse, center, middle
background-image: url(https://images.unsplash.com/photo-1509081438789-63838f150db7?ixlib=rb-4.0.3&ixid=MnwxMjA3fDB8MHxwaG90by1wYWdlfHx8fGVufDB8fHx8&auto=format&fit=crop&w=387&q=80)
background-size: cover

# ma206distributions and ma206equations

---
class: inverse, middle, center

# Hello!

---
class: inverse, middle, center

#   Thank you for your willingess to have a look at some of the work we are doing in `ma206distributions` and `ma206equations`!

---
class: inverse, middle, center

#  Mathematical fluency involves frequent use of probability distributions and of course equations.

---
class: inverse, middle, center
#  However, visualizing these distributions with software and typing equations can be tedious.

---
class: inverse, middle, center
#    In a well-defined statistics and probability curriculum, the set of distributions and equations to be mastered is known and limited.
---
class: inverse, middle, center
#   The goal of this project is to provide ready-to-use functions that will make it easier to engage computationally with these distributions.

---
class: inverse, middle, center
#   In what follows, we highlight and demo some of the functionality.

---
class: inverse, middle, center
#   Your feedback is on this work is greatly appreciated.

---
class: inverse, middle, center
#   Without further ado...

</style>

---
class: inverse, center, middle

# tidy_dbinom()

## The function tidy_dbinom() returns a dataframe that pairs outcomes and probabilities, using just two inputs. View source code [here](https://github.com/EvaMaeRey/ma206distributions/blob/main/R/tidy_dbinom.R).

---

```r
*library(tidyverse)
```
]
 
.panel2-tidy_dbinom-auto[

]

---
count: false
 
### tidy_dbinom() usage
.panel1-tidy_dbinom-auto[

```r
library(tidyverse)
*library(ma206distributions)
```
]
 
.panel2-tidy_dbinom-auto[

]

---
count: false
 
### tidy_dbinom() usage
.panel1-tidy_dbinom-auto[

```r
library(tidyverse)
library(ma206distributions)
*library(ma206equations)
```
]
 
.panel2-tidy_dbinom-auto[

]

---
count: false
 
### tidy_dbinom() usage
.panel1-tidy_dbinom-auto[

```r
library(tidyverse)
library(ma206distributions)
library(ma206equations)

*tidy_dbinom(single_trial_prob = 1/6,
*           num_trials = 8)
```
]
 
.panel2-tidy_dbinom-auto[

```
# A tibble: 9 × 4
  num_successes probability single_trial_prob num_trials
          <int>       <dbl>             <dbl>      <dbl>
1             0 0.233                   0.167          8
2             1 0.372                   0.167          8
3             2 0.260                   0.167          8
4             3 0.104                   0.167          8
5             4 0.0260                  0.167          8
6             5 0.00417                 0.167          8
7             6 0.000417                0.167          8
8             7 0.0000238               0.167          8
9             8 0.000000595             0.167          8
```
]

---
count: false
 
### tidy_dbinom() usage
.panel1-tidy_dbinom-auto[

```r
library(tidyverse)
library(ma206distributions)
library(ma206equations)

tidy_dbinom(single_trial_prob = 1/6,
            num_trials = 8) ->
*eight_die_rolls
```
]
 
.panel2-tidy_dbinom-auto[

]

---
count: false
 
### tidy_dbinom() usage
.panel1-tidy_dbinom-auto[

```r
library(tidyverse)
library(ma206distributions)
library(ma206equations)

tidy_dbinom(single_trial_prob = 1/6,
            num_trials = 8) ->
eight_die_rolls

*tidy_dbinom(single_trial_prob = .5,
*           num_trials = 10)
```
]
 
.panel2-tidy_dbinom-auto[

```
# A tibble: 11 × 4
   num_successes probability single_trial_prob num_trials
           <int>       <dbl>             <dbl>      <dbl>
 1             0    0.000977               0.5         10
 2             1    0.00977                0.5         10
 3             2    0.0439                 0.5         10
 4             3    0.117                  0.5         10
 5             4    0.205                  0.5         10
 6             5    0.246                  0.5         10
 7             6    0.205                  0.5         10
 8             7    0.117                  0.5         10
 9             8    0.0439                 0.5         10
10             9    0.00977                0.5         10
11            10    0.000977               0.5         10
```
]

---
count: false
 
### tidy_dbinom() usage
.panel1-tidy_dbinom-auto[

```r
library(tidyverse)
library(ma206distributions)
library(ma206equations)

tidy_dbinom(single_trial_prob = 1/6,
            num_trials = 8) ->
eight_die_rolls

tidy_dbinom(single_trial_prob = .5,
            num_trials = 10) ->
*ten_coin_flips
```
]
 
.panel2-tidy_dbinom-auto[

]

---
count: false
 
### tidy_dbinom() usage
.panel1-tidy_dbinom-auto[

```r
library(tidyverse)
library(ma206distributions)
library(ma206equations)

tidy_dbinom(single_trial_prob = 1/6,
            num_trials = 8) ->
eight_die_rolls

tidy_dbinom(single_trial_prob = .5,
            num_trials = 10) ->
ten_coin_flips

*tidy_dbinom(single_trial_prob = 1/38,
*           num_trials = 3)
```
]
 
.panel2-tidy_dbinom-auto[

```
# A tibble: 4 × 4
  num_successes probability single_trial_prob num_trials
          <int>       <dbl>             <dbl>      <dbl>
1             0   0.923                0.0263          3
2             1   0.0748               0.0263          3
3             2   0.00202              0.0263          3
4             3   0.0000182            0.0263          3
```
]

---
count: false
 
### tidy_dbinom() usage
.panel1-tidy_dbinom-auto[

```r
library(tidyverse)
library(ma206distributions)
library(ma206equations)

tidy_dbinom(single_trial_prob = 1/6,
            num_trials = 8) ->
eight_die_rolls

tidy_dbinom(single_trial_prob = .5,
            num_trials = 10) ->
ten_coin_flips

tidy_dbinom(single_trial_prob = 1/38,
            num_trials = 3) ->
*three_roulette_spins
```
]
 
.panel2-tidy_dbinom-auto[

]

---
count: false
 
### tidy_dbinom() usage
.panel1-tidy_dbinom-auto[

```r
library(tidyverse)
library(ma206distributions)
library(ma206equations)

tidy_dbinom(single_trial_prob = 1/6,
            num_trials = 8) ->
eight_die_rolls

tidy_dbinom(single_trial_prob = .5,
            num_trials = 10) ->
ten_coin_flips

tidy_dbinom(single_trial_prob = 1/38,
            num_trials = 3) ->
three_roulette_spins
```
]
 
.panel2-tidy_dbinom-auto[

]

---
class: inverse, center, middle

# geom_lollipop(), scale_x_counting(), geom_fulcrum

## The dataframe that tidy_dbinom() creates can easily be fed into the popular ggplot2 visualization system.  Visualization functions geom_lollipop() and scale_x_counting() help concisely visualize discrete probability visualizations. geom_fulcrum() marks the balancing point of the data - which is the expected value.

---

count: false
 
### geom_lollipop() and scale_x_counting() usage
.panel1-tidy_dbinom_plot-auto[

```r
*library(ma206distributions)
```
]
 
.panel2-tidy_dbinom_plot-auto[

]