Econometrics Review Questions

(38) The joint density function of two continuous random variables x and
c 2 x y 2 x 6, 0 y 5
f x,
y
0
otherwise
Find the following;
(i) The value of the constant c
(ii) The marginal distribution functions for x and y
(iii) The marginal density functions for x and y
(iv) P3 x 4, y 2
(v) Px
3
(vi) Px
y 4
(39) The joint density function of two continuous random variables x and
cxy 0 x 4, 1 y 5
f x,
y
0 otherwise
Find the following;
(i) The value of the constant c
P 1 x 2, 2 y 3
(ii)
(iii) Px
3, y 2
(iv) The marginal distribution function for X if 0x
4
(v) The marginal distribution function for Y if 1 y
5
(40) The joint density function of the random variables X and Y is given by
8 xy 0 x 1, 0 y x
f x,
y
0 otherwise
Find: (a) The marginal density of X
(b) The marginal density of Y
(c) The conditional density of X
(d) The condition density of Y
y is given by
y is given by
(41) The joint pdf of two random variables X and Y is given by
k 0 y x1
f x,
y
0 otherwise
Where k is a constant.
(a) Determine the value of k
(b) Find the marginal pdfs of X and Y
P 0 x 1 , 0 y
1
(c) Find
2 2
6