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EN.560 (2)
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Midterm

# Exam Solutions Spring 2014Exam

Department
EN.560
Course Code
EN.560.348
Professor
All
Study Guide
Midterm

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J ]
(No Name -1)
2>
_____ 03/13/14
1. (5
pts)
For a continuous random variable
X,
the probability density function is given by
I(x) ~ { ~x2
O::=;
x::=;
3
(1)
otherwise
(a)
(2
pts)
Determine the value of c.
')
'3
C.
Y-..,5 \ )
-:::-
~c.,
~~
) ('t-.·
L
d'f.. -:
~!
o
-
0
'V
(b) (3
pts)
Find the expected value of
X.
'5
'3
EC~)~
~o
( ~2
"/.-..'-1
\
~-Sl
'I- ~ ')
d't-
~
-
-
~lt>
0
7
2.
(5
pts)
Consider the events
A, B,
C.
A
=
{10,12,15,17,18}
B
=
{12, 13, 14}
C
=
{13, 13.5, 14, 15.5}
S :::.\
10
I
11
I \:, I
I?
I) \ \
l1
I \
S
1
1)".
t) \ \'1 \ \ ~ 1
(a) (2
pts)
Among events
A, B,
and C, which two are mutually exclusive?
f\
n
C
=
>6
\~c]/
(b) (3
pts)
Determine the sample points in
(A
U C)
n
Be.
"6
c. ::-
f )
\l
I \). ') I
I"') \ \ ~ -
S )
11
Ii)
1
A
u c ~ ~\\)\
n \ \")
I \
3 \
J
I
Y \
J
C; \
It;.
<)
I
Ii
I
1.81
li\\JL)f)
eO ~
t\\),13.'),I'l,\').';-,
\~,U