# Question: suppose the joint probability distribution of two binary random variables...

###### Question details

Suppose the joint probability distribution of two binary random variables X and Y are given as follows.

x/y | 1 | 2 |

0 | 3/10 | 0 |

1 | 4/10 | 3/10 |

X goes along side as 0 and 1, Y goes along top as 1 and 2.

a) Show the marginal distribution of X.

b) Find entropy H(Y ).

c) Find conditional entropy H(X|Y ) and H(Y |X).

d) Find mutual information I(X; Y ).

e) Find joint entropy H(X, Y ).

f) Suppose X and Y are independent. Show that H(X|Y ) = H(X).

g) Suppose X and Y are independent. Show that H(X, Y ) = H(X) + H(Y ).

h) Show that I(X; X) = H(X).