(2) (5 points) The joint probability function of two discrete random variables x and Y is
given by
f(x,y)=c(2x+y)
where x and y can take all integers such that 0<=x<=2,0<=y<=3, and f(x,y)=0
otherwise.
(a) Find the value of c.
(b) Find P(x>=1,Y<=2).
(c) Show that the random variables x and Y are not independent. Since we are
disproving independence, we can do that by simply finding an example where
P(x=x,Y=y)!=P(x=x)P(Y=y)
(2) (5 points) The joint probability function of two discrete random variables X and Y is given by f(x,y)=c2x+y)
where x and y can take all integers such that 0 x 2,0 y 3, and f(x,y) = 0 otherwise.
0
2
Totals 1
Y
1
3
X
0
0
c
2c
3c
6c
1
2c
3c
4c
5c
14c
2
4c
5c
6c
7c
22c
Totals 1
6c
9c
12c
15c
42c
(a) Find the value of c.
(b) Find P(X > 1,Y < 2).
(c) Show that the random variables X and Y are not independent. Since we are disproving independence, we can do that by simply finding an example where
P(X=x,Y =y) P(X=x)P(Y =y)