Thread: another joint distribution question

P(X=x,Y=y)=1/8 for x =3,5 and y=1,2,4,7
P(X=x,Y=y)=0 otherwise
a) What is Fxy(x,y) for all x,y in R
b) What is pxy(x,y) for all x,y in R
c) What is px(x) for all x in R
d) What is py(y) for all y in R
e) What is the the marginal cdf Fx(x) for all x in R
f) What is the the marginal cdf Fy(y) for all y in R

My attempt
----------
a)

Fxy(x,y) =
y<1 1<=y<2 2<=y<4 4<=y<7 y<=7
x<3 0 0 0 0 0
3<=x<5 0 1/8 2/8 4/8 6/8
x<=5 0 2/8 4/8 6/8 8/8

1 if otherwise

b)

Pxy(X=x,Y=y)= 1/8 if x is 3,5 and y is 1,2,4,7
0 otherwise

c)

Originally Posted by Sneaky

P(X=x,Y=y)=1/8 for x =3,5 and y=1,2,4,7
P(X=x,Y=y)=0 otherwise
a) What is Fxy(x,y) for all x,y in R
b) What is pxy(x,y) for all x,y in R
c) What is px(x) for all x in R
d) What is py(y) for all y in R
e) What is the the marginal cdf Fx(x) for all x in R
f) What is the the marginal cdf Fy(y) for all y in R

My attempt
----------
a)

Fxy(x,y) =
y<1 1<=y<2 2<=y<4 4<=y<7 y<=7
x<3 0 0 0 0 0
3<=x<5 0 1/8 2/8 4/8 6/8
x<=5 0 2/8 4/8 6/8 8/8

1 if otherwise

b)

Pxy(X=x,Y=y)= 1/8 if x is 3,5 and y is 1,2,4,7
0 otherwise

c)

X and Y are both discrete distributions. I suggest you format your answers using a table or grid.

here is a clear pic


is what I did for a and b right?


for e)
Fx(x)=
0 if x<3
1/2 if 3<=x<5
2/2 if x<=5
1 otherwise
for f)
Fy(y)=
0 if y<1
1/4 if 1<=y<2
2/4 if 2<=y<4
3/4 if 4<=y<7
4/4 if y<=7
1 otherwise