discrete probability

# discrete probability
## Using flipbookr and xaringan
### Me

---

@media print {
  .has-continuation {
    display: block;
  }
}

code.r.hljs.remark-code{
  position: relative;
  overflow-x: hidden;
}

code.r.hljs.remark-code:hover{
  overflow-x:visible;
  width: 500px;
  border-style: solid;
}
</style>

---

```r
*knitr::opts_chunk$set(echo = TRUE)
```
]
 
.panel2-setup-auto[

]

---

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

]

---
count: false

```r
library(tidyverse)
*c(3800, 200, 0, -100, - 300)
```
]
 
.panel2-roulette-auto[

```
[1] 3800  200    0 -100 -300
```
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
* data.frame(payout = .)
```
]
 
.panel2-roulette-auto[

```
  payout
1   3800
2    200
3      0
4   -100
5   -300
```
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
* mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38))
```
]
 
.panel2-roulette-auto[

```
  payout       prob
1   3800 0.02631579
2    200 0.13157895
3      0 0.15789474
4   -100 0.31578947
5   -300 0.36842105
```
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
* mutate(ev_contribution = prob*payout)
```
]
 
.panel2-roulette-auto[

```
  payout       prob ev_contribution
1   3800 0.02631579       100.00000
2    200 0.13157895        26.31579
3      0 0.15789474         0.00000
4   -100 0.31578947       -31.57895
5   -300 0.36842105      -110.52632
```
]

---
count: false

```
  payout       prob ev_contribution        ev
1   3800 0.02631579       100.00000 -15.78947
2    200 0.13157895        26.31579 -15.78947
3      0 0.15789474         0.00000 -15.78947
4   -100 0.31578947       -31.57895 -15.78947
5   -300 0.36842105      -110.52632 -15.78947
```
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
* mutate(var_contribution = (payout - ev)^2 * prob )
```
]
 
.panel2-roulette-auto[

```
  payout       prob ev_contribution        ev var_contribution
1   3800 0.02631579       100.00000 -15.78947     383164.45546
2    200 0.13157895        26.31579 -15.78947       6126.98644
3      0 0.15789474         0.00000 -15.78947         39.36434
4   -100 0.31578947       -31.57895 -15.78947       2239.39350
5   -300 0.36842105      -110.52632 -15.78947      29759.44015
```
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
* mutate(variance = sum(var_contribution))
```
]
 
.panel2-roulette-auto[

```
  payout       prob ev_contribution        ev var_contribution variance
1   3800 0.02631579       100.00000 -15.78947     383164.45546 421329.6
2    200 0.13157895        26.31579 -15.78947       6126.98644 421329.6
3      0 0.15789474         0.00000 -15.78947         39.36434 421329.6
4   -100 0.31578947       -31.57895 -15.78947       2239.39350 421329.6
5   -300 0.36842105      -110.52632 -15.78947      29759.44015 421329.6
```
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
* mutate(sd = sqrt(variance))
```
]
 
.panel2-roulette-auto[

```
  payout       prob ev_contribution        ev var_contribution variance       sd
1   3800 0.02631579       100.00000 -15.78947     383164.45546 421329.6 649.0991
2    200 0.13157895        26.31579 -15.78947       6126.98644 421329.6 649.0991
3      0 0.15789474         0.00000 -15.78947         39.36434 421329.6 649.0991
4   -100 0.31578947       -31.57895 -15.78947       2239.39350 421329.6 649.0991
5   -300 0.36842105      -110.52632 -15.78947      29759.44015 421329.6 649.0991
```
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
*roulette_example
```
]
 
.panel2-roulette-auto[

]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
roulette_example

*roulette_example
```
]
 
.panel2-roulette-auto[

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
roulette_example

roulette_example %>%
* ggplot()
```
]
 
.panel2-roulette-auto[
![](discrete_probability_flipbook_files/figure-html/roulette_auto_12_output-1.png)
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
roulette_example

roulette_example %>%
  ggplot() +
* aes(x = payout, y = prob)
```
]
 
.panel2-roulette-auto[
![](discrete_probability_flipbook_files/figure-html/roulette_auto_13_output-1.png)
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
roulette_example

roulette_example %>%
  ggplot() +
  aes(x = payout, y = prob) +
* geom_point()
```
]
 
.panel2-roulette-auto[
![](discrete_probability_flipbook_files/figure-html/roulette_auto_14_output-1.png)
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
roulette_example

roulette_example %>%
  ggplot() +
  aes(x = payout, y = prob) +
  geom_point() +
* geom_segment(aes(xend = payout, yend = 0))
```
]
 
.panel2-roulette-auto[
![](discrete_probability_flipbook_files/figure-html/roulette_auto_15_output-1.png)
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
roulette_example

roulette_example %>%
  ggplot() +
  aes(x = payout, y = prob) +
  geom_point() +
  geom_segment(aes(xend = payout, yend = 0)) +
* geom_rect(aes(xmin = 0, xmax = payout,
*               ymin = 0, ymax = prob),
*           alpha = .2)
```
]
 
.panel2-roulette-auto[
![](discrete_probability_flipbook_files/figure-html/roulette_auto_16_output-1.png)
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
roulette_example

roulette_example %>%
  ggplot() +
  aes(x = payout, y = prob) +
  geom_point() +
  geom_segment(aes(xend = payout, yend = 0)) +
  geom_rect(aes(xmin = 0, xmax = payout,
                ymin = 0, ymax = prob),
            alpha = .2) +
* geom_vline(xintercept = -15.789, linetype = "dashed")
```
]
 
.panel2-roulette-auto[
![](discrete_probability_flipbook_files/figure-html/roulette_auto_17_output-1.png)
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
roulette_example

roulette_example %>%
  ggplot() +
  aes(x = payout, y = prob) +
  geom_point() +
  geom_segment(aes(xend = payout, yend = 0)) +
  geom_rect(aes(xmin = 0, xmax = payout,
                ymin = 0, ymax = prob),
            alpha = .2) +
  geom_vline(xintercept = -15.789, linetype = "dashed") ->
*picture_ev
```
]
 
.panel2-roulette-auto[

]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
roulette_example

roulette_example %>%
  ggplot() +
  aes(x = payout, y = prob) +
  geom_point() +
  geom_segment(aes(xend = payout, yend = 0)) +
  geom_rect(aes(xmin = 0, xmax = payout,
                ymin = 0, ymax = prob),
            alpha = .2) +
  geom_vline(xintercept = -15.789, linetype = "dashed") ->
picture_ev

*roulette_example
```
]
 
.panel2-roulette-auto[

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
roulette_example

roulette_example %>%
  ggplot() +
  aes(x = payout, y = prob) +
  geom_point() +
  geom_segment(aes(xend = payout, yend = 0)) +
  geom_rect(aes(xmin = 0, xmax = payout,
                ymin = 0, ymax = prob),
            alpha = .2) +
  geom_vline(xintercept = -15.789, linetype = "dashed") ->
picture_ev

roulette_example %>%
* ggplot()
```
]
 
.panel2-roulette-auto[
![](discrete_probability_flipbook_files/figure-html/roulette_auto_20_output-1.png)
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
roulette_example

roulette_example %>%
  ggplot() +
  aes(x = payout, y = prob) +
  geom_point() +
  geom_segment(aes(xend = payout, yend = 0)) +
  geom_rect(aes(xmin = 0, xmax = payout,
                ymin = 0, ymax = prob),
            alpha = .2) +
  geom_vline(xintercept = -15.789, linetype = "dashed") ->
picture_ev

roulette_example %>%
  ggplot() +
* aes(x = payout - ev, y = payout - ev)
```
]
 
.panel2-roulette-auto[
![](discrete_probability_flipbook_files/figure-html/roulette_auto_21_output-1.png)
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
roulette_example

roulette_example %>%
  ggplot() +
  aes(x = payout, y = prob) +
  geom_point() +
  geom_segment(aes(xend = payout, yend = 0)) +
  geom_rect(aes(xmin = 0, xmax = payout,
                ymin = 0, ymax = prob),
            alpha = .2) +
  geom_vline(xintercept = -15.789, linetype = "dashed") ->
picture_ev

roulette_example %>%
  ggplot() +
  aes(x = payout - ev, y = payout - ev) +
* geom_point()
```
]
 
.panel2-roulette-auto[
![](discrete_probability_flipbook_files/figure-html/roulette_auto_22_output-1.png)
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
roulette_example

roulette_example %>%
  ggplot() +
  aes(x = payout, y = prob) +
  geom_point() +
  geom_segment(aes(xend = payout, yend = 0)) +
  geom_rect(aes(xmin = 0, xmax = payout,
                ymin = 0, ymax = prob),
            alpha = .2) +
  geom_vline(xintercept = -15.789, linetype = "dashed") ->
picture_ev

roulette_example %>%
  ggplot() +
  aes(x = payout - ev, y = payout - ev) +
  geom_point() +
* coord_equal()
```
]
 
.panel2-roulette-auto[
![](discrete_probability_flipbook_files/figure-html/roulette_auto_23_output-1.png)
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
roulette_example

roulette_example %>%
  ggplot() +
  aes(x = payout, y = prob) +
  geom_point() +
  geom_segment(aes(xend = payout, yend = 0)) +
  geom_rect(aes(xmin = 0, xmax = payout,
                ymin = 0, ymax = prob),
            alpha = .2) +
  geom_vline(xintercept = -15.789, linetype = "dashed") ->
picture_ev

roulette_example %>%
  ggplot() +
  aes(x = payout - ev, y = payout - ev) +
  geom_point() +
  coord_equal() +
* geom_segment(aes(xend = payout - ev, yend = 0))
```
]
 
.panel2-roulette-auto[
![](discrete_probability_flipbook_files/figure-html/roulette_auto_24_output-1.png)
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
roulette_example

roulette_example %>%
  ggplot() +
  aes(x = payout, y = prob) +
  geom_point() +
  geom_segment(aes(xend = payout, yend = 0)) +
  geom_rect(aes(xmin = 0, xmax = payout,
                ymin = 0, ymax = prob),
            alpha = .2) +
  geom_vline(xintercept = -15.789, linetype = "dashed") ->
picture_ev

roulette_example %>%
  ggplot() +
  aes(x = payout - ev, y = payout - ev) +
  geom_point() +
  coord_equal() +
  geom_segment(aes(xend = payout - ev, yend = 0)) +
* geom_rect(aes(xmin = ev, xmax = payout - ev,
*               ymin = 0, ymax = payout - ev,
*           alpha = prob))
```
]
 
.panel2-roulette-auto[
![](discrete_probability_flipbook_files/figure-html/roulette_auto_25_output-1.png)
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
roulette_example

roulette_example %>%
  ggplot() +
  aes(x = payout, y = prob) +
  geom_point() +
  geom_segment(aes(xend = payout, yend = 0)) +
  geom_rect(aes(xmin = 0, xmax = payout,
                ymin = 0, ymax = prob),
            alpha = .2) +
  geom_vline(xintercept = -15.789, linetype = "dashed") ->
picture_ev

roulette_example %>%
  ggplot() +
  aes(x = payout - ev, y = payout - ev) +
  geom_point() +
  coord_equal() +
  geom_segment(aes(xend = payout - ev, yend = 0)) +
  geom_rect(aes(xmin = ev, xmax = payout - ev,
                ymin = 0, ymax = payout - ev,
            alpha = prob)) +
* geom_rect(aes(xmin = 0, ymin = 0, xmax = sd, ymax = sd),
*           fill = "darkred")
```
]
 
.panel2-roulette-auto[
![](discrete_probability_flipbook_files/figure-html/roulette_auto_26_output-1.png)
]

---
count: false

```r
library(tidyverse)
c(3800, 200, 0, -100, - 300) %>%
  data.frame(payout = .) %>%
  mutate(prob = c(1/38, 5/38, 6/38, 12/38, 14/38)) %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
roulette_example

roulette_example %>%
  ggplot() +
  aes(x = payout, y = prob) +
  geom_point() +
  geom_segment(aes(xend = payout, yend = 0)) +
  geom_rect(aes(xmin = 0, xmax = payout,
                ymin = 0, ymax = prob),
            alpha = .2) +
  geom_vline(xintercept = -15.789, linetype = "dashed") ->
picture_ev

roulette_example %>%
  ggplot() +
  aes(x = payout - ev, y = payout - ev) +
  geom_point() +
  coord_equal() +
  geom_segment(aes(xend = payout - ev, yend = 0)) +
  geom_rect(aes(xmin = ev, xmax = payout - ev,
                ymin = 0, ymax = payout - ev,
            alpha = prob)) +
  geom_rect(aes(xmin = 0, ymin = 0, xmax = sd, ymax = sd),
            fill = "darkred") ->
*picture_variance
```
]
 
.panel2-roulette-auto[

]

---

```r
*c(20000, 5000, 0)
```
]
 
.panel2-insurance-auto[

```
[1] 20000  5000     0
```
]

---
count: false

```r
c(20000, 5000, 0) %>%
* data.frame(payout = .)
```
]
 
.panel2-insurance-auto[

```
  payout
1  20000
2   5000
3      0
```
]

---
count: false

```r
c(20000, 5000, 0) %>%
  data.frame(payout = .) %>%
* mutate(situation = c("car totaled",
*                      "car repairs",
*                      "no accidents"))
```
]
 
.panel2-insurance-auto[

```
  payout    situation
1  20000  car totaled
2   5000  car repairs
3      0 no accidents
```
]

---
count: false

```r
c(20000, 5000, 0) %>%
  data.frame(payout = .) %>%
  mutate(situation = c("car totaled",
                       "car repairs",
                       "no accidents")) %>%
* mutate(prob = c(1/100, 9/100, 90/100))
```
]
 
.panel2-insurance-auto[

```
  payout    situation prob
1  20000  car totaled 0.01
2   5000  car repairs 0.09
3      0 no accidents 0.90
```
]

---
count: false

```r
c(20000, 5000, 0) %>%
  data.frame(payout = .) %>%
  mutate(situation = c("car totaled",
                       "car repairs",
                       "no accidents")) %>%
  mutate(prob = c(1/100, 9/100, 90/100))  %>%
* mutate(ev_contribution = prob*payout)
```
]
 
.panel2-insurance-auto[

```
  payout    situation prob ev_contribution
1  20000  car totaled 0.01             200
2   5000  car repairs 0.09             450
3      0 no accidents 0.90               0
```
]

---
count: false

```
  payout    situation prob ev_contribution  ev
1  20000  car totaled 0.01             200 650
2   5000  car repairs 0.09             450 650
3      0 no accidents 0.90               0 650
```
]

---
count: false

```r
c(20000, 5000, 0) %>%
  data.frame(payout = .) %>%
  mutate(situation = c("car totaled",
                       "car repairs",
                       "no accidents")) %>%
  mutate(prob = c(1/100, 9/100, 90/100))  %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
* mutate(var_contribution = (payout - ev)^2 * prob )
```
]
 
.panel2-insurance-auto[

```
  payout    situation prob ev_contribution  ev var_contribution
1  20000  car totaled 0.01             200 650          3744225
2   5000  car repairs 0.09             450 650          1703025
3      0 no accidents 0.90               0 650           380250
```
]

---
count: false

```r
c(20000, 5000, 0) %>%
  data.frame(payout = .) %>%
  mutate(situation = c("car totaled",
                       "car repairs",
                       "no accidents")) %>%
  mutate(prob = c(1/100, 9/100, 90/100))  %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
* mutate(variance = sum(var_contribution))
```
]
 
.panel2-insurance-auto[

```
  payout    situation prob ev_contribution  ev var_contribution variance
1  20000  car totaled 0.01             200 650          3744225  5827500
2   5000  car repairs 0.09             450 650          1703025  5827500
3      0 no accidents 0.90               0 650           380250  5827500
```
]

---
count: false

```r
c(20000, 5000, 0) %>%
  data.frame(payout = .) %>%
  mutate(situation = c("car totaled",
                       "car repairs",
                       "no accidents")) %>%
  mutate(prob = c(1/100, 9/100, 90/100))  %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
* mutate(sd = sqrt(variance))
```
]
 
.panel2-insurance-auto[

```
  payout    situation prob ev_contribution  ev var_contribution variance       sd
1  20000  car totaled 0.01             200 650          3744225  5827500 2414.022
2   5000  car repairs 0.09             450 650          1703025  5827500 2414.022
3      0 no accidents 0.90               0 650           380250  5827500 2414.022
```
]

---
count: false

```r
c(20000, 5000, 0) %>%
  data.frame(payout = .) %>%
  mutate(situation = c("car totaled",
                       "car repairs",
                       "no accidents")) %>%
  mutate(prob = c(1/100, 9/100, 90/100))  %>%
  mutate(ev_contribution = prob*payout) %>%
  mutate(ev = sum(ev_contribution)) %>%
  mutate(var_contribution = (payout - ev)^2 * prob ) %>%
  mutate(variance = sum(var_contribution)) %>%
  mutate(sd = sqrt(variance)) ->
*insurance_example
```
]
 
.panel2-insurance-auto[

]