ECON 409
Home Assignment 1
Spring 2014
Q1
Consider a Bernoulli random variable. Specically, X cfw_0, 1 and P r(X = 1) = and
P r(X = 0) = 1 .
1. Obtain the population mean and variance of the distribution.
2. Suppose X1 , X2 , ., Xn are independent observa
ECON 409
Home Assignment 2
Spring 2014
Q1
We are given the non-random matrices
1 0.3 21
1 0.1 21
X = 1 0.2 3 ,
1 0.5 3
1 0.4 3
am the vector of random disturbances,
u =
u1
u2
u3
u4
u5
Y =
84
73
65
68
85
,
.
1. Calculate the following matrices: X X, X
ECON 409
Midterm I
Spring 2014
Question 1 (25 points)
Suppose X is N (, 2 ). Find the pdf of Y = exp(X).
Solution:
fX (x) =
1 e
2 2
(x)2
2 2
. Remark: < X < +.
Method
Method I: for y 0, FY (y) = P r(Y y) = P r(exp(X) y) = P r(X
ln(y) = FX (ln(y). fY