Probability - Lab 4

library(tidyverse)
library(openintro)

Exercise 1

A streak of length 1 would be making 1 shot and then missing the next shot. A streak of length 0 is missing a shot when your previous shot is also a miss.

kobe_streak <- calc_streak(kobe_basket$shot)

Exercise 2

The distribution of Kobe’s streaks is right skewed and peaks at 0. The median is length 0 and the mean is length 0.76. Based on this information the typical streak length is 0. His longest streak of baskets was 4

kobe_streak %>%
  summarise(
    mean_streak = mean(length),
    median_streak = median(length)
  )

##   mean_streak median_streak
## 1   0.7631579             0

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

### Exercise 3

Simulating the flipping of an unfair coin gives me 26 heads and 74 tails. Pretty close to the probability.

set.seed(35797)  
coin_outcomes <- c("heads", "tails")
sim_fair_coin <- sample(coin_outcomes, size = 100, replace = TRUE, prob = c(0.2, 0.8))
table(sim_fair_coin)

## sim_fair_coin
## heads tails 
##    26    74

Exercise 4

We need to set the size to 133 to simulate 133 shots. Then, we change the probability to 45% and 55% to replicate Kobe’s overall shooting percentage.

set.seed(35797) 
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 
## 63 70

Exercise 5

sim_streak = calc_streak(sim_basket)

Exercise 6

The distribution is right skewed and the typical observation is a streak of length 0. The longest streak is 6 hits long in my simiulation, which is longer the Kobe’s maximum streak.

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

Exercise 7

I would expect it to be different, but be very similar in shape and distribution. 133 shots is large enough in size to reproduce similar result almost every time.

Exercise 8

The simulated results have a longer tail with higher streak than Kobe’s. Comparing Kobe’s results to a simulation I would say we can debunk the hot hand theory here.