Let X be a random variable with values in t1, 2, 3u and Y a random variable with values in t1, 2, 3, 4u. Initially we have the following partial information about their joint probability mass function pX,Y px, yq: x y 1 2 3 4 pX pX|Y "4 1 2/20 0 1/20 3/20 2 0 2/20 3/20 3 3/20 pY 4/20 2/20 6/20 Compute the missing values of the joint probability mass function, the missing values for the probability mass functions pX of X and pY of Y , respectively, as well as determine the conditional distribution of X given Y " 4 (i.e. the values of the conditional probability mass function pX|Y "4 ).

Problem 1.2 [H] points} Let X be a random variable with values in {1,2,3} and Y a random variable with valnm in {1,23, 4}. Initially we have the following partial information about their joint probability mass function pLy-(s, y): y 1 2 3 4 PX PX|F=4 311: you the Elfin IE'ompute the missing values of the joint probability mass function, the missing values for the probability mass functions pix of X and 31;: of 1", respectively, as 1well as determine the conditional distribution of X given Y = 4 [i.e. the values of the oontiitional probability mass function PX|Y=4l