ECON 425 ASSIGNMENT 1 S. C. Ahn
DUE SEPTEMBER 6 (THURSDAY)
Show your effort. No credit will be given if no appropriate explanation follows.
1. (10 pts.) Let Y be a random variable distributed as shown in the accompanying table.
y 1 2 3 4
f(y) .1 .2 .3 .4
Find E(y) and var(y).
2. (70 pts.) The joint probability distribution of X and Y is given by the following table: (For
example, f(4,9) = 0.)
x\y
1
3
9
2
1/8
1/24
1/12
4
1/4
1/4
0
6
1/8
1/24
1/12
(1) Derive the marginal pdfs of X and Y.
(2) Determine whether X and Y are stochastically independent or not.
(3) Compute population means of X and Y.
(4) Compute population variances of X and Y.
(5) Compute the correlation coefficient between X and Y.
(6) Check whether or not Pr(X = 2|Y = 9) = Pr(Y = 9|X = 2).
(7) Given X = 2, find the population mean of Y, i.e., E(Y|X = 2)
[Hint: E(Y|X = 2) = Σyyf(y|x=2)].
3. (20 pts.) Let X ~ N(2,9), Z ~ N(0,1), Y ~ χ2(4) and W ~ χ2(5). Assume that all of the
random variables X, Z, Y and W are stochastically independent.
(1) Find Pr(X < 6).
(2) Find Pr(Y < 9.49).
(3) Find
(
)
Pr 3.75 / 4ZY>.
(4) Find 5
Pr 5.19
4
Y
W
⎛⎞
>
⎜⎟
⎝⎠
.