A. Mathematics: Consider a classification problem where we wish to determine if a human subject is likely to get a concussion in the next year. We use four features X1 (Age), x2 (concussHistory), x; (FavoriteSport), X4 (Gender) . Each feature takes on one ofa discrete number of values, shown below: Age Child Teen Adult concussHistory Never Recent DecadesAgo FavoriteSport Boxing Golf Rugby Baseball Gender Male Female We wish to classify each user as either yi=LikelyConcuss or yi=NotLike yConcuss. 1. How can the features above be transformed to use a logistic classier? For each feature, use a transformation that reasonably captures the structure of the data while minimizing the number of parameters to learn. 2. How many parameters are required to learn a separating hyper-plane (w and any other necessary elements) for logistic classification with the features converted in question 1? (Work from your answer to question 1. If you could not figure out question 1, assume we have a new space of 8 continuous numeric features X1, xZ, X3 this may or may not be a valid result from question 2.] 3. A vector x is said to have "unit magnitude\" ifo'x = 1. Which of the following vectors has approximate unit magnitude, 0.8 S VxTx s 1.2 ? 2 0.4 1 0.3 (a) ['01] (b) l 05,5 (c) H (d) [39,5 0.5 0.7 0 0.6 4. What is the projection (dot product) of the vectors below onto the vectorx = 0.2 70.3 0.5 0.8 2 0.5 (a) (1] (bl if 0 1,5 5. In class, we define the logistic/sigmoid function as g(h) = 1+:_h,producingthe curve in solid blue shown to the right. Note while g(h)z0 when h is a very low negative number (h4), when h is close to zero, 2 .95 only when h>20. Provide an exact algebraic formula for ga"2(h) to fit this specification. 0 2 6. Let us assume we have a classifier with w = 4 and b = 2. Provide two distinct inputs xi , 1 1 one that would be firmly classified In class 1 and one that would be firmly classified In class 0 (IwaI > 100)