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)