Lab_3_Probability

library(tidyverse)
library(openintro)

Exercise 1

What does a streak length of 1 mean,i.e how many hits and misses in a streak of 1? What about a streak length of 0? Answer: A streak lenth of 1 means the player hits the basket once and that of 0 means no hits.

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

Exercise 2

The distribution of Kobe’s streak length is twisted to get shooting streak. The typical streak length of 0 occours approximately by count 40 and that of 1 is with the count near 25. The longest shooting streak length of 4 was found at count 1.

Exercise 3

set.seed(3847)  # make sure to change the seed
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" "heads" "tails" "tails" "tails" "tails" "heads" "tails" "heads"
##  [10] "heads" "tails" "heads" "tails" "tails" "heads" "heads" "heads" "heads"
##  [19] "tails" "heads" "heads" "heads" "heads" "tails" "heads" "tails" "heads"
##  [28] "tails" "heads" "heads" "heads" "heads" "tails" "heads" "tails" "heads"
##  [37] "heads" "tails" "heads" "heads" "heads" "tails" "heads" "heads" "tails"
##  [46] "tails" "heads" "tails" "heads" "heads" "tails" "heads" "tails" "heads"
##  [55] "heads" "tails" "heads" "tails" "tails" "heads" "tails" "heads" "tails"
##  [64] "tails" "tails" "tails" "tails" "heads" "tails" "heads" "tails" "tails"
##  [73] "heads" "heads" "tails" "heads" "heads" "heads" "tails" "tails" "tails"
##  [82] "heads" "heads" "tails" "tails" "heads" "tails" "heads" "tails" "tails"
##  [91] "tails" "tails" "tails" "heads" "heads" "tails" "heads" "heads" "heads"
## [100] "tails"

table(sim_fair_coin)

## sim_fair_coin
## heads tails 
##    52    48

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 
##    18    82

Exercise 4

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

Exercise 5

set.seed(1975)
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

library(ggplot2)
sim_basket <- sample(shot_outcomes, size = 133, replace = TRUE, prob = c(0.45,0.55))
sim_streak <-calc_streak(sim_basket)
ggplot(data =sim_streak, aes(x = length)) + geom_bar()

summary(calc_streak(sim_basket))

##      length      
##  Min.   :0.0000  
##  1st Qu.:0.0000  
##  Median :0.0000  
##  Mean   :0.5952  
##  3rd Qu.:1.0000  
##  Max.   :5.0000

Exercise 7

I already expected the outcomes of distribution is slightly different from above question because data frames are not the same even though shooting percentage is identical.

Exercise 8

The distributions look very similar and right skewed.. Therefore, there is no evidence that the hot hand model fits Kobe’s shooting patterns.