Bayes vs 1NN classififier. 1 Id like to collect some Pokemon of which to do battle. Without knowing much, and my primary criteria is to fifind Pokemon who can throw things to a very far distance. In particular, I will only accept Pokemon who can throw trajectories at least 72 inches (6 ft) distance.

In general, if a Pokemon says he/she can throw x inches, then in truth they are lying, and their true ability follows a Gaussian distribution with mean x and variance 2 = 62 = 36 inches.

For parts (a) and (b), you may use wolframalpha.com to help compute the integral. Report both the symbolic form and the computed number up to 3 signifificant digits. (We will fifirst try to match your numbers, and if your numbers are incorrect, we will use the symbolic form for partial credit.)

(a) Arbok claims that he can throw 70 inches. What is the probability that he fulfifills my criteria?

(b) Bulbasaur claims he can throw 60 inches. What is the probability that he is can actually throw further than Arbok? (Assume their throwing arms are independent.)

(c) Charmander is the next Pokemon who crosses my path, and he claims to throw exactly 72 inches. Consider the following reward function: If I accept him, and Charmander does fulfifill this criteria, then he wins tons of battles and I get +10 reward. If he in fact is not fulfifilling my critiera, I waste my resources, he loses battles, and I end up with a deadbeat Pokemon, translating to a 1 reward. If I reject Charmander and in fact was able to throw far enough, then someone else will scoop him up and destroy my other Pokemon, giving me a 25 reward. But if I reject Charmander and he was in fact unable, there is 0 reward. Think of loss as negative reward.

i. What is the Bayes risk of accepting vs rejecting?

ii. What does the Bayes classififier tell me to do?

(d) Diglett, Eevee, and Flareon are former Pokemons of mine, who have all lied about their abilities. Diglett wrote he throws 85 inches but actually he can only throw 60 inches. Eevee wrote she throws 72 inches and in fact she throws closer to 70 inches. Flareon wrote 90 inches and its not a bad estimate; he throws 89 inches. Think of these three Pokefriends as my training dataset. Gardevoir suddenly appears and walks across my keyboard. I ask him How far can you throw your projectiles? and he sniffffs, and says 82 inches, easily. Does a 1-nearest neighbor regressor predict that Gardevoir fulfifills my critiria? Explain your answer.