Math and Statistics Lab 2

download.file("http://www.openintro.org/stat/data/kobe.RData", destfile = "kobe.RData")

load("kobe.RData")


head(kobe)

##    vs game quarter time
## 1 ORL    1       1 9:47
## 2 ORL    1       1 9:07
## 3 ORL    1       1 8:11
## 4 ORL    1       1 7:41
## 5 ORL    1       1 7:03
## 6 ORL    1       1 6:01
##                                               description basket
## 1                 Kobe Bryant makes 4-foot two point shot      H
## 2                               Kobe Bryant misses jumper      M
## 3                        Kobe Bryant misses 7-foot jumper      M
## 4 Kobe Bryant makes 16-foot jumper (Derek Fisher assists)      H
## 5                         Kobe Bryant makes driving layup      H
## 6                               Kobe Bryant misses jumper      M

kobe$basket[1:9]

## [1] "H" "M" "M" "H" "H" "M" "M" "M" "M"

Streak of length of 1 means that there was one hit and one miss. Length of 0 means there was one miss and no hits

kobe_streak<-calc_streak(kobe$basket)

barplot(table(kobe_streak))

It looks like Poisson with lambda 1. Typical streak length was either 0 or 1 (0 was more likely). Longest one was 4 hits and 1 miss.

outcomes <- c("heads","tails")

sample(outcomes, size=1, replace=TRUE)

## [1] "heads"

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

sim_fair_coin

##   [1] "tails" "tails" "tails" "heads" "heads" "heads" "heads" "heads"
##   [9] "tails" "tails" "heads" "tails" "tails" "heads" "tails" "tails"
##  [17] "tails" "heads" "heads" "tails" "heads" "heads" "tails" "heads"
##  [25] "heads" "tails" "tails" "heads" "tails" "tails" "heads" "heads"
##  [33] "heads" "heads" "tails" "heads" "heads" "tails" "tails" "tails"
##  [41] "tails" "heads" "heads" "heads" "heads" "tails" "heads" "heads"
##  [49] "tails" "tails" "tails" "heads" "tails" "tails" "heads" "heads"
##  [57] "tails" "tails" "heads" "heads" "tails" "heads" "heads" "heads"
##  [65] "heads" "tails" "tails" "heads" "tails" "heads" "tails" "tails"
##  [73] "heads" "tails" "tails" "heads" "heads" "tails" "tails" "tails"
##  [81] "tails" "heads" "heads" "tails" "heads" "tails" "heads" "heads"
##  [89] "heads" "heads" "heads" "tails" "heads" "heads" "heads" "heads"
##  [97] "tails" "tails" "tails" "heads"

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

table(sim_unfair_coin)

## sim_unfair_coin
## heads tails 
##    15    85

There were 18 heads

?sample

## starting httpd help server ... done

outcomes<-c("H","M")

sim_basket<-sample(outcomes,size=1,replace=TRUE)

sim_basket<-sample(outcomes, size =133, replace=TRUE, prob=c(0.45,0.55))

kobe$basket

##   [1] "H" "M" "M" "H" "H" "M" "M" "M" "M" "H" "H" "H" "M" "H" "H" "M" "M"
##  [18] "H" "H" "H" "M" "M" "H" "M" "H" "H" "H" "M" "M" "M" "M" "M" "M" "H"
##  [35] "M" "H" "M" "M" "H" "H" "H" "H" "M" "H" "M" "M" "H" "M" "M" "H" "M"
##  [52] "M" "H" "M" "H" "H" "M" "M" "H" "M" "H" "H" "M" "H" "M" "M" "M" "H"
##  [69] "M" "M" "M" "M" "H" "M" "H" "M" "M" "H" "M" "M" "H" "H" "M" "M" "M"
##  [86] "M" "H" "H" "H" "M" "M" "H" "M" "M" "H" "M" "H" "H" "M" "H" "M" "M"
## [103] "H" "M" "M" "M" "H" "M" "H" "H" "H" "M" "H" "H" "H" "M" "H" "M" "H"
## [120] "M" "M" "M" "M" "M" "M" "H" "M" "H" "M" "M" "M" "M" "H"

sim_basket

##   [1] "H" "H" "M" "M" "M" "M" "M" "H" "H" "M" "M" "H" "M" "M" "M" "M" "M"
##  [18] "M" "H" "M" "H" "H" "M" "H" "H" "M" "M" "H" "M" "H" "H" "M" "M" "M"
##  [35] "H" "H" "M" "H" "H" "M" "H" "M" "H" "M" "M" "M" "H" "M" "M" "H" "M"
##  [52] "M" "H" "H" "M" "M" "H" "M" "H" "M" "M" "M" "H" "M" "H" "M" "M" "M"
##  [69] "M" "M" "M" "M" "M" "M" "M" "H" "H" "M" "M" "M" "H" "M" "M" "H" "M"
##  [86] "M" "M" "M" "M" "H" "H" "M" "M" "H" "H" "M" "H" "H" "M" "M" "M" "H"
## [103] "H" "M" "M" "M" "M" "M" "M" "M" "M" "H" "M" "H" "M" "H" "H" "H" "M"
## [120] "H" "M" "M" "M" "M" "H" "H" "M" "M" "H" "M" "M" "M" "M"

On my own

sim_streak<-calc_streak(sim_basket)

barplot(table(sim_streak))

Distribution is very right skewed. With a small peak at 2. The typical streak length is 0. The longest streak was 6.

I would expect distribution to be somewhat simular. It most likely would not be exactly the same but it should be simular with simular mean.

Kobe had more shot with steak length of 1. It does not look like Kobe had the hot hand. If he did distribution of his streaks would have longer tail. However, his ditribution has very short tail.

Math and Statistics Lab 2

Mikhail Groysman

October 12, 2018