13) Two random variables, X and Y, have a joint probability density function ofthe form
f(x,y) = k(x+2y) 0<=x<=1, 0<=y<=1 = 0 elsewhere
Find
a) the value of k for which this is a valid joint probability density function
b) the conditional probability that X is greater than 1/2 given that Y = 1/2
c) the conditional probability that Y is less than, or equal to, 1/2 given that X is 1/2. 2