1. Given two random variables X and Y and their joint distribution P(X,Y): X = 2 X = 4 X = 6 Y = Red (2) 0.18 0.15 0.07 Y = Blue (4) 0.15 0.05 0.15 Y = Green (6) 0.04 0.16 0.05 Find: 1.a) H(X) (10 points) 1.b) H(Y) (10 points) 1.c.) D(X||Y) (10 points) 1.d) D(Y||X) (10 points) 1.e) H(X|Y) (10 points) 1.f) H(Y|X) (10 points) 1.g) H(X,Y) (10 points) 1.h) H(Y) - H(Y|X) (10 points) 1.i) I(X;Y) (10 points) 1.j) If X is the number of wheels on a vehicle and Y is the color of the vehicle, what does I(X;Y) tell us? (Let's say we can observe the number of wheels easily but not the color) (10 points)