Lab 3 Probability

library(tidyverse)
library(openintro)

Exercise 1

What does a streak length of 1 mean, i.e. how many hits and misses are in a streak of 1? What about a streak length of 0?

A streak length of 1 means that the shooter shot 1 basket or hit before missing the next few shots. A streak length of 0 means that the shooter made no hits or scored consecutive misses without any hits.

Exercise 2

The distribution of kobe’s streak length appears to be right-skewed where most of the data is concentrated on the streak lengths of 1 and 0.Kobe’s typical streak length is 0 with a count of around 38 or 39 and his streak length of 1 is around a count of 23 or 24. His longest streak of baskets is 4 with a count of 1.

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

Exercise 3

In my simulation of flipping the unfair coin 100 time I had got 14 heads and 86 tails

set.seed(1997)              # make sure to change the seed
coin_outcomes <- c("heads", "tails")
sample(coin_outcomes, size = 1, replace = TRUE)

## [1] "tails"

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 
##    14    86

Exercise 4

I adjusted the sample function to reflect a percentage of 45% to sample 133 shots.

shot_outcomes <- c("H", "M")
sim_basket <- sample(shot_outcomes, size = 133, replace = TRUE,prob=c(0.45,0.65))

Exercise 5

set.seed(3)
shot_outcomes <- c("H", "M")
sim_basket <- sample(shot_outcomes, size = 133, replace = TRUE,prob=c(0.45,0.55))
sim_streak <- calc_streak(sim_basket)

Exercise 6

The distribution of the streak length is skewed to the right again and the typical streak is 0 with shoots around 40. In this simulation the player’s longest streak was 5 and it was only occurred once.

library(ggplot2)
ggplot(data=sim_streak,aes(x=length))+
  geom_bar()

Exercise 7

If I were to run the simulation a second time I would expect the streak distribution to be the same because the probablity of the number of hits is 45% we should expect to hit more misses than hits in those 133 total shots. So as a result we should not be too surprised if the shooter goes on a long streak of length 0 because the odds of missing are favored more than the number of hits.

Exercise 8:

They seem to be fairly similar they both tend to go on long streaks of length 0 a lot and the second highest would be a streak length of 1. The bar graphs also show that they are both skewed to the right and barely go on long streaks of length greater than 1. I believe the hot hand model fits Kobe’s shooting patterns because running the simulation a couple of times I can see that though there may slight diffrences the data more or less looks similar to Kobe’s shooting patterns.