Homework SourseY is a uniform discrete RV over 1 2 3 X is dependent on y an
Y is a uniform discrete RV over {1, 2, 3}. X is dependent on y and spans 1 to y. So, if y = 3, X = {1, 2, 3}; if y = 2, X = {1, 2}, etc. Find P[X = 2]![Y is a uniform discrete RV over {1, 2, 3}. X is dependent on y and spans 1 to y. So, if y = 3, X = {1, 2, 3}; if y = 2, X = {1, 2}, etc. Find P[X = 2]Solutionp](/WebImages/12/y-is-a-uniform-discrete-rv-over-1-2-3-x-is-dependent-on-y-an-1011278-1761522060-0.webp "Y is a uniform discrete RV over {1, 2, 3}. X is dependent on y and spans 1 to y. So, if y = 3, X = {1, 2, 3}; if y = 2, X = {1, 2}, etc. Find P[X = 2]Solutionp")
Solution
probability of y=1 =>1/3
P(Y=2)=1/3
P(Y=3)=1/3
so X=2 occurs when Y=3 and 2
probability of X=2 in Y=3=> 1/3*1/3=1/9
P(X=2) when Y=2=> 1/3*1/2=1/6
P(X=2)= 1/9+1/6 = 5/18
