Lab 3
Kathleen Vern
2/4/2019
Exercise 1:
A streak length of one means one shot was made “in a row” followed by a miss, while zero means he did not hit the shot to start a “streak.”
Exercise 2:
The distribution is unimodal and right skewed showing Kobe’s streak lengths in the 2009 NBA finals. Thiis shows that his typical streak length was actually 0 due to a high number of consecutive misses. In contrast, his longest streak was 4 consecutively made baskets.
https://labs-az-02.oit.duke.edu:30623/graphics/plot.png?width=574&height=300&randomizer=-692228935
Exercise 3:
The code for sampling the fair coin gave 46 heads, but 24 heads in the unfair coin.
set.seed(03021999)
coin_outcomes <- c("heads", "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
## 24 76sim_unfair_coin heads tails 24 76
Exercise 4:
To make the sample function a shooting percentage of 45% for a sample size of 133, you change the size variable from 1 to 133 and then need to reassign the percentages of H = 45% and M = 55% by rewriting the “prob = c(0.45, 0.55)”
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
## 59 74sim_basket H M 60 73
Exercise 5:
## length
## 1 0
## 2 1
## 3 0
## 4 0
## 5 0
## 6 1
## 7 1
## 8 3
## 9 3
## 10 1
## 11 2
## 12 0
## 13 1
## 14 0
## 15 0
## 16 1
## 17 0
## 18 0
## 19 1
## 20 0
## 21 0
## 22 0
## 23 3
## 24 0
## 25 0
## 26 0
## 27 2
## 28 0
## 29 0
## 30 0
## 31 1
## 32 0
## 33 2
## 34 0
## 35 2
## 36 0
## 37 0
## 38 1
## 39 1
## 40 0
## 41 2
## 42 1
## 43 0
## 44 0
## 45 0
## 46 1
## 47 1
## 48 0
## 49 0
## 50 1
## 51 1
## 52 0
## 53 1
## 54 1
## 55 0
## 56 0
## 57 0
## 58 1
## 59 2
## 60 0
## 61 0
## 62 2
## 63 1
## 64 0
## 65 0
## 66 0
## 67 0
## 68 4
## 69 4
## 70 0
## 71 3
## 72 0
## 73 0
## 74 1
## 75 5Exercise 6:
The typical streak length for this simulated independent shooter with a 45% shooting percentage is 0. The longest streak calculated varies depending on the simulation however it ranges from 4-8 consecutive baskets within our lab group.
https://labs-az-02.oit.duke.edu:30623/graphics/plot.png?width=574&height=300&randomizer=257193770
Exercise 7:
We would expect the streak distribution to be mostly similar: the results will still be the same, i.e., the player’s typical streak length will still be zero and their highest score will be around 4. However, due to variations in the simulation, the frequency of each hit will change somewhat. Data from our lab partners proves that running the simulation of the independent shooters various times leads to varying distributions and differences in maximum streak lengths. This is also shown through a more common study of flipping a coin 100 times, as the results would not be expected to be exactly 50 heads and 50 tails each trial. Similarly, each simulation will vary within the output of our code as it would in a non-virtual experiment.
Exercise 8:
Kobe’s data shows a similar trend to that of the 45% success rate however with each varying simulation there are higher streaks and varying numbers of 0, 1 and 2 basket streaks.That being said, both of the histograms demonstrate a unimodal, right skewed graph with its’ mode at 0 and median around 1.