Winter 06
1
Econometrics
ASSIGNMENT 1
100 POINTS TOTAL
DUE: Thursday, January 26, 3:20 p.m.
**IMPORTANT REMINDER: LATE ASSIGNMENTS CANNOT BE ACCEPTED – NO EXCEPTIONS**
Note
:
Questions 1~3 are simple and straightforward. Questions 4 & 5 are also simple, albeit long. Questions 7 & 8 are on
hypothesis testing.
1.
[5]
Let
X
be the random variable distributed as Normal (5,4). Find the probabilities of the following events:
(i)
P(
X
≤
6)
(ii)
P(
X
> 4)
(iii)
P(
X
– 5 > 1)
2.
[5]
Let
X
denote the prison sentence, in years, for people convicted of auto theft in California. Suppose that the
pdf
of
X
is given by
2
1
9
( )
( )
,0
3.
=
<
<
f x
x
x
Use integration to find the expected prison sentence. [
hint
: requires calculus.]
3.[5]
Let
X
denote the annual salary on university professors in the United States, measured in
thousands of dollars
.
Suppose that the average salary is 52.3, with a standard deviation of 14.6. Find the mean and standard deviation
when salary is measured in
dollars
.
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 Three '11
 ProJim
 Econometrics, Variance, Probability theory, probability density function, average liquor consumption

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