Lab 3

library(tidyverse)
library(openintro)

Exercise 1

A streak of 1 means 1 hit. A streak of zero means a miss.

Exercise 2

kobe_streak <- calc_streak(kobe_basket$shot)
ggplot(data = kobe_streak, aes(x = length)) +
  geom_bar()

The distribution is right-skewed. The typical streak length was 0 and the longest streak is 4.

Exercise 3

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

## [1] "tails"

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

sim_fair_coin

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

table(sim_fair_coin)

## sim_fair_coin
## heads tails 
##    50    50

set.seed(989) 
sim_unfair_coin <- sample(coin_outcomes, size = 100, replace = TRUE, 
                          prob = c(0.2, 0.8))
table(sim_unfair_coin)

## sim_unfair_coin
## heads tails 
##    11    89

Only 11 times did the unfair coin come up heads.

Exercise 4

What change needs to be made to the sample function so that it reflects a shooting percentage of 45%? Make this adjustment, then run a simulation to sample 133 shots. Assign the output of this simulation to a new object called sim_basket.

set.seed(100)
shot_outcomes <- c("H", "M")
sim_basket <- sample(shot_outcomes, size = 133, replace = TRUE, prob=c(0.45, 0.55))
table(sim_basket)

## sim_basket
##  H  M 
## 61 72

I added the seed so the values did not change.

Exercise 5

sim_streak <- calc_streak(sim_basket)

Exercise 6

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

Distribution is right-skewed, longest streak was 6 and typical streak was 0.

Exercise 7

I would expect a similar distribution.

Exercise 8

The distributions are somewhat similar between Kobe and the simulation. The longest streak is somewhat different which lets me to believe Kobe doesn’t fit the hot hand model.