ECI 114
Fall 2010
Name _____________________________
Midterm 1 Solutions (100 points):
October 20, 2010
SHOW your work.
It is not necessary to give a final numerical answer like “12” unless
specifically asked; you just need to have the correct expression like “4!/2!”.
Please circle or
otherwise highlight your answer.
Turn in your “crib sheet” with your exam.
GOOD LUCK!
_____________________________________________________________________________
_
1.
For each of the following statements, circle the letter “T” if it is true and “F” if it is false.
(14 points)
T
F
a.
For a certain sample of 25 observations and a mean of 10, it is known that
Σ
y
i
2
= 2625.
The variance of this sample is 5.
2
.
5
24
125
24
10
*
25
2625
1
2
2
2
2
=
=

=


=
∑
N
Y
N
y
s
i
T
F
b.
If A and B are collectively exhaustive, then Pr(A
∪
B) = Pr(A) + Pr(B).
Would be true if A and B are
mutually exclusive
, since Pr(A∩B) =
∅
.
T
F
c.
If events A, B, and C are independent, then Pr(A) = Pr(A
∩
B
∩
C)/Pr(B
∩
C).
If events A, B, and C are independent,[Pr(A
∩
B
∩
C]=Pr(A)Pr(B)Pr(C)=Pr(A)Pr(B
∩
C)
T
F
d.
If S = {the outcome of the roll of a balanced die} = {1, 2, 3, 4, 5, 6}, then the
set containing the two events {(E
∪
P’), (P
∩
O)}, where P = prime, E = even,
O = odd, is a partition of S (count 1 as a prime).
P={1,2,3,5}; E={2,4,6}; O={1,3,5}.
E
∪
P’={2,4,6}, P
∩
O={1,3,5}.
Because these two sets are ME and CE, they constitute a partition.
T
F
e.
For any event A, (A
∩
S)
∪
(A’
∩
S) = S, where S represents the entire sample
space.
A
∩
S = A, A’
∩
S = A’, and A
∪
A’ = S by definition of complement.
T
F
f.
Since the expectation operator is linear, E[5X
2
] = 5E[X*X] = 5(E[X])
2
.
X