Question

3.. Given two random variables X and Y and their joint distribution P(X,Y) (6 points each) :
X = 2 X = 4 X = 6
Y = 2 0.14 0.14 0.06
Y = 4 0.17 0.17 0.15
Y = 6 0.02 0.1 0.05
Find (include the calculations):

H(X)
H(Y)
D(X||Y)
D(Y||X)
H(X|Y)
H(Y|X)
H(X,Y)
H(Y) - H(Y|X)
I(X;Y)

Answer 1

Explanation:

Given two random variables X and Y and their joint distribution P(X,Y) (6 points each) : X = 2 X = 4 X = 6 Y = 2 0.14 0.14 0.06 Y = 40.17 0.17 0.15 Y = 6 0.02 0.1 0.05 Find: A. H(X) B. H(Y) C. D( XY) D. D(Y|X) E. H(XY) F. H(YX) G. H(X,Y) H. HY) - HY|X) I. I(X;Y)