- 1 -
University of Colorado
Department of Economics
Economics 3818
Midterm Examination
Prof. Jeffrey S. Zax
27 September 2005
Solutions
(14)
1.
Consider two outcomes C and D, where Pr(C)=.3, Pr(D)=.5, Pr(C
1
D)=.3
(3)
a.
What is Pr(C
c
D)? Why?
Pr(C
c
D)
= Pr(C) + Pr(D)
!
Pr(C
1
D)
= .3 + .5
!
.3
= .5
(3)
b.
What is Pr(C
*
D)?
Pr(C
*
D)
= Pr(C
1
D)
'
Pr(D)
= .3
'
.5
= 3
'
5
(2)
c.
What is Pr(D
*
C)?
Pr(D
*
C)
= Pr(C
1
D)
'
Pr(C)
= .3
'
.3
= 1
(2)
d.
Would you expect Pr(C
*
D) and Pr(D
*
C) to be the same? Why or why not?
Ordinarily they would not be the same. They share the same numerator,
Pr(C
1
D)
, but their denominators would usually be different. They would be
equal only if the numerator were zero or if Pr(C)=Pr(D).
(2)
e,
Are C and D mutually exclusive? Why or why not?
C and D are not mutually exclusive because the probability of their intersection
is not zero.
(2)
f.
Are C and D independent? Why or why not?
C and D are not independent because
.3 = P(C)
…
P(C|D) = 3
'
5.

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*