Question 1: Describe the distribution of streak lengths.
Distribution of Kobe's streak lengths is right skewed.
Distribution of Independent shooter's streal lengths is also right skewed.
Question 2: What is the typical streak length for this?
Typical streak length of Kobe is 0. Typical streak length of Indipendent shooter is also 0.
Question 3: Simulated independent shooter with a 45% shooting percentage? How long is the player's longest streak
Independent shooters longest streak length is 5 in my simulation.
Question 4: What is the number of baskets in 133 shots?
table(sim_basket)
Independent shooter's number of baskets in 133 shots is 62 in my simulation.
Question 5: If you were to run the simulation of the independent shooter a second time, how would you expect its streak distribution to compare to the distribution from the question above? Exactly the same? Somewhat similar? Totally different? Explain your reasoning.
I would expect the streak distribution to be somewhat similar because we are defining a fixed propability of 45%, so every time we run the simulation it would give streaks based on probability, so it would generate somewhat similar result for every run.
Question 6: How does Kobe Bryant's distribution of streak lengths compare to the distribution of streak lengths for the simulated shooter? Using this comparison, do you have evidence that the hot hand model fits Kobe's shooting patterns? Explain.
Distribution of Kobe Bryant's streak lengths and Independent shooter's streak lengths are both right skewed. Number of 0 length streaks and 1 length streaks of Kobe are higher than that of Independent shooter's. The number of streak lenghts of 2 and more of Kobe are also higher than Independent shooter's but Independent shooter has larger streak lengths than Kobe which mean Independent shooter has more hits in sequence than Kobe. Independent shooter's streak lengths are computer simulated, so we can assume that they are generated randomly, where as Kobe's streak lengths are the real time data.
Both of their distributions are almost similar and Independent shooter has longer streaks than Kobe. My assumption is that if a randomly generated data and Kobe's data are producing similar results, we can assume that Kobe doesn't fit hot hand model because if we say he fits, then random computer generated data should also be considered as hot hand which we know is not true.