Get access to the Probablity Lab
kobe<-read.csv("C:\\Users\\lizza\\Documents\\CUNY - Data Analytics\\DATA 606 - Probablity and Statistics\\Week 2 Lab\\kobe.csv")
#Use the head function to obtain the first several rows of a data matrix or data frame
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#Sequence of hits and misses from his 9 shot attemtpts in the first quarter
kobe$basket[1:9]## [1] H M M H H M M M M
## Levels: H MWhat does a streak length of 1 mean, i.e. how many hits and misses are in a streak of 1? What about a streak length of 0?
#Received error
#Error in calc_streak(kobe$basket) : could not find function "calc_streak"
#kobe_streak <- calc_streak(kobe$basket)
#barplot(table(kobe_streak))Describe the distribution of Kobe’s streak lengths from the 2009 NBA finals. What was his typical streak length? How long was his longest streak of baskets?
Simulations in R
#R creates rando numbers to simulate flipping a fair coin
outcomes <-c("heads","tails")
sample(outcomes, size=1, replace=TRUE)## [1] "heads"#The vector outcomes can be thought of as a hat with two slips of paper in it: one slip says heads and the other says tails. The function sample draws one slip from the hat and tells us if it was a head or a tail.
#The size argument tells R how many samples to draw
#Replace=TRUE indicates we put the slip of paper back in the hat before drawing againsim_fair_coin <-sample(outcomes, size=100, replace=TRUE)
sim_fair_coin## [1] "tails" "tails" "tails" "tails" "heads" "tails" "tails" "tails"
## [9] "heads" "heads" "tails" "heads" "tails" "tails" "tails" "tails"
## [17] "tails" "tails" "tails" "heads" "tails" "heads" "tails" "heads"
## [25] "tails" "tails" "heads" "heads" "tails" "tails" "heads" "heads"
## [33] "tails" "heads" "heads" "heads" "tails" "heads" "heads" "heads"
## [41] "tails" "tails" "tails" "tails" "heads" "tails" "tails" "tails"
## [49] "heads" "tails" "tails" "tails" "tails" "heads" "heads" "tails"
## [57] "heads" "heads" "heads" "tails" "heads" "heads" "heads" "heads"
## [65] "heads" "heads" "tails" "heads" "heads" "tails" "tails" "heads"
## [73] "tails" "heads" "heads" "heads" "tails" "tails" "heads" "heads"
## [81] "tails" "heads" "tails" "tails" "heads" "tails" "heads" "tails"
## [89] "heads" "heads" "tails" "heads" "heads" "tails" "tails" "tails"
## [97] "heads" "tails" "tails" "heads"table(sim_fair_coin)## sim_fair_coin
## heads tails
## 47 53#Say we're trying to simulate an unfair coin that we know only lands heads 20% of the time. We can adjust for this by adding an argument called prob, which provides a vector of two probability weights.
sim_unfair_coin <-sample(outcomes, size=100, replace=TRUE, prob=c(0.2,0.8))
sim_unfair_coin## [1] "heads" "tails" "tails" "tails" "tails" "tails" "heads" "tails"
## [9] "tails" "tails" "heads" "tails" "tails" "tails" "tails" "tails"
## [17] "tails" "tails" "tails" "tails" "tails" "tails" "tails" "tails"
## [25] "tails" "heads" "tails" "heads" "tails" "heads" "tails" "tails"
## [33] "tails" "tails" "tails" "tails" "tails" "heads" "tails" "tails"
## [41] "tails" "tails" "tails" "tails" "tails" "tails" "tails" "tails"
## [49] "tails" "tails" "tails" "tails" "heads" "tails" "tails" "tails"
## [57] "tails" "tails" "tails" "tails" "tails" "heads" "heads" "tails"
## [65] "tails" "heads" "tails" "tails" "heads" "tails" "tails" "tails"
## [73] "tails" "tails" "tails" "tails" "tails" "tails" "heads" "tails"
## [81] "heads" "tails" "tails" "heads" "heads" "tails" "tails" "tails"
## [89] "tails" "heads" "heads" "heads" "tails" "tails" "tails" "tails"
## [97] "tails" "tails" "tails" "tails"table(sim_unfair_coin)## sim_unfair_coin
## heads tails
## 19 81#Heads will have a probability of 20% and tails 80%In your simulation of flipping the unfair coin 100 times, how many flips came up heads?
Tails populated 74 times while Heads populated 26
Simulating the Independent Shooter
#To simulate a single shot from an independent shooter with a shooting percentage of 50% we type
outcomes <- c("H","M")
sim_basket <- sample(outcomes, size=1, replace= TRUE)
sim_basket## [1] "M"table(sim_basket)## sim_basket
## M
## 1What 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.
outcomes <- c("H","M")
sim_basket <- sample(outcomes, size=133, replace=TRUE, prob=c(0.45,0.55))
sim_basket## [1] "M" "M" "H" "H" "H" "M" "H" "H" "H" "M" "H" "H" "H" "H" "H" "H" "H"
## [18] "M" "H" "M" "M" "H" "H" "M" "M" "M" "M" "M" "H" "M" "H" "M" "M" "M"
## [35] "M" "M" "M" "M" "M" "M" "H" "H" "M" "M" "M" "H" "M" "M" "H" "H" "M"
## [52] "M" "M" "M" "H" "H" "M" "H" "H" "H" "H" "M" "H" "H" "M" "M" "M" "M"
## [69] "M" "M" "M" "M" "M" "M" "M" "M" "M" "H" "M" "M" "M" "M" "H" "H" "H"
## [86] "M" "H" "H" "M" "M" "M" "H" "M" "M" "H" "H" "H" "H" "H" "H" "H" "M"
## [103] "M" "H" "H" "H" "H" "M" "M" "M" "H" "M" "H" "M" "M" "M" "M" "H" "M"
## [120] "M" "M" "M" "M" "H" "H" "M" "M" "M" "H" "H" "M" "M" "M"table(sim_basket)## sim_basket
## H M
## 56 77Comparison
kobe$basket## [1] H M M H H M M M M H H H M H H M M H H H M M H M H H H M M M M M M H M
## [36] H M M H H H H M H M M H M M H M M H M H H M M H M H H M H M M M H M M
## [71] M M H M H M M H M M H H M M M M H H H M M H M M H M H H M H M M H M M
## [106] M H M H H H M H H H M H M H M M M M M M H M H M M M M H
## Levels: H Msim_basket## [1] "M" "M" "H" "H" "H" "M" "H" "H" "H" "M" "H" "H" "H" "H" "H" "H" "H"
## [18] "M" "H" "M" "M" "H" "H" "M" "M" "M" "M" "M" "H" "M" "H" "M" "M" "M"
## [35] "M" "M" "M" "M" "M" "M" "H" "H" "M" "M" "M" "H" "M" "M" "H" "H" "M"
## [52] "M" "M" "M" "H" "H" "M" "H" "H" "H" "H" "M" "H" "H" "M" "M" "M" "M"
## [69] "M" "M" "M" "M" "M" "M" "M" "M" "M" "H" "M" "M" "M" "M" "H" "H" "H"
## [86] "M" "H" "H" "M" "M" "M" "H" "M" "M" "H" "H" "H" "H" "H" "H" "H" "M"
## [103] "M" "H" "H" "H" "H" "M" "M" "M" "H" "M" "H" "M" "M" "M" "M" "H" "M"
## [120] "M" "M" "M" "M" "H" "H" "M" "M" "M" "H" "H" "M" "M" "M"