Lab 3: Probability

Load packages

library(tidyverse)
library(openintro)

Data

glimpse(kobe_basket)

## Rows: 133
## Columns: 6
## $ vs          <fct> ORL, ORL, ORL, ORL, ORL, ORL, ORL, ORL, ORL, ORL, ORL, ORL…
## $ game        <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
## $ quarter     <fct> 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3…
## $ time        <fct> 9:47, 9:07, 8:11, 7:41, 7:03, 6:01, 4:07, 0:52, 0:00, 6:35…
## $ description <fct> Kobe Bryant makes 4-foot two point shot, Kobe Bryant misse…
## $ shot        <chr> "H", "M", "M", "H", "H", "M", "M", "M", "M", "H", "H", "H"…

Exercise 1

A streak length of 1 means that 1 basket was made before a miss. A streak length of 0 means that no baskets were made.

kobe_streak <- calc_streak(kobe_basket$shot)

ggplot(data = kobe_streak, aes(x = length)) +
  geom_bar()

Exercise 2

The distribution of Kobe’s streak lengths from the 2009 NBA finals were skewed right. He had a higher frequency of streak lengths of 0 and 1. His lower frequency of streak lengths were in the ranges of 2 to 4. His typical streak length was 0, and his longest streak of baskets was 4. All this can be determined from the plot found above.

Simulations in R

coin_outcomes <- c("heads", "tails")
sample(coin_outcomes, size = 1, replace = TRUE)

## [1] "heads"

sim_fair_coin <- sample(coin_outcomes, size = 100, replace = TRUE)

sim_fair_coin

##   [1] "tails" "tails" "tails" "tails" "heads" "tails" "heads" "tails" "tails"
##  [10] "heads" "heads" "tails" "tails" "tails" "heads" "heads" "heads" "heads"
##  [19] "heads" "heads" "tails" "tails" "heads" "tails" "tails" "heads" "tails"
##  [28] "heads" "heads" "tails" "heads" "tails" "tails" "heads" "heads" "tails"
##  [37] "tails" "heads" "tails" "heads" "heads" "tails" "heads" "heads" "tails"
##  [46] "heads" "heads" "heads" "heads" "tails" "heads" "heads" "heads" "tails"
##  [55] "tails" "tails" "tails" "heads" "heads" "heads" "tails" "tails" "heads"
##  [64] "tails" "tails" "heads" "heads" "heads" "heads" "tails" "heads" "heads"
##  [73] "tails" "tails" "tails" "tails" "tails" "heads" "heads" "tails" "tails"
##  [82] "heads" "heads" "heads" "heads" "tails" "tails" "heads" "heads" "tails"
##  [91] "heads" "heads" "heads" "tails" "tails" "tails" "tails" "heads" "heads"
## [100] "heads"

table(sim_fair_coin)

## sim_fair_coin
## heads tails 
##    53    47

set.seed(431811)                 # make sure to change the seed

sim_unfair_coin <- sample(coin_outcomes, size = 100, replace = TRUE, 
                          prob = c(0.2, 0.8))

Exercise 3

sim_unfair_coin

##   [1] "tails" "tails" "tails" "tails" "tails" "tails" "heads" "tails" "tails"
##  [10] "tails" "tails" "tails" "tails" "tails" "tails" "heads" "tails" "tails"
##  [19] "tails" "heads" "heads" "tails" "tails" "tails" "tails" "tails" "tails"
##  [28] "tails" "tails" "tails" "heads" "tails" "heads" "tails" "heads" "heads"
##  [37] "tails" "tails" "tails" "tails" "tails" "heads" "heads" "tails" "tails"
##  [46] "heads" "tails" "tails" "heads" "tails" "tails" "tails" "heads" "tails"
##  [55] "tails" "tails" "tails" "tails" "tails" "heads" "tails" "tails" "tails"
##  [64] "tails" "heads" "heads" "heads" "tails" "tails" "tails" "tails" "tails"
##  [73] "tails" "tails" "tails" "tails" "heads" "tails" "heads" "tails" "tails"
##  [82] "tails" "tails" "heads" "tails" "heads" "tails" "tails" "tails" "tails"
##  [91] "tails" "heads" "heads" "tails" "tails" "tails" "tails" "heads" "tails"
## [100] "tails"

table(sim_unfair_coin)

## sim_unfair_coin
## heads tails 
##    24    76

24 flips came up ‘heads’.

?sample

Simulating the Independent Shooter

shot_outcomes <- c("H", "M")
sim_basket <- sample(shot_outcomes, size = 1, replace = TRUE)

Exercise 4

The sample probability for ‘H’ should be changed to 0.45, and ‘M’ to 0.65.

shot_outcomes <- c("H", "M")
sim_basket <- sample(shot_outcomes, size = 133, replace = TRUE, prob = c(0.45, 0.55))
sim_basket

##   [1] "H" "M" "H" "M" "H" "H" "H" "H" "M" "H" "M" "H" "H" "H" "M" "H" "M" "M"
##  [19] "H" "H" "H" "H" "H" "M" "M" "H" "H" "H" "H" "M" "M" "M" "H" "M" "H" "H"
##  [37] "M" "H" "H" "H" "M" "H" "H" "H" "M" "H" "M" "H" "H" "M" "M" "M" "M" "H"
##  [55] "H" "H" "H" "H" "H" "M" "H" "M" "M" "H" "M" "M" "M" "M" "M" "H" "M" "M"
##  [73] "M" "M" "H" "H" "M" "H" "M" "M" "H" "M" "H" "H" "M" "H" "H" "H" "M" "H"
##  [91] "H" "M" "M" "M" "H" "M" "M" "M" "M" "M" "H" "M" "M" "M" "M" "H" "M" "M"
## [109] "M" "M" "M" "M" "M" "H" "M" "M" "H" "M" "H" "M" "M" "M" "M" "H" "H" "M"
## [127] "H" "H" "M" "M" "M" "M" "H"

table(sim_basket)

## sim_basket
##  H  M 
## 63 70