STAT
35000
InClassActivity
10

Page
2
of
2
Instructor:
]
Sarkar
e
3.
Arandom
variable
Xhasapdf
f(x)
=
x/2
when0<x<2,and
0
otherwise.
(a)
(1
point)
Calculate
the
expected
value
of
X.
"
2
X
E("Lj'jx"o%dx
=
%T

o
—
°
—
7
(b)
(2
points)
Finally
find
the
variance
of
X,
a2=
V
(X)
=
E[(X

u)?]
=
E(X?)

[E(X)]3.
(ny2(%)=2
%3
(c)
(1
point)
Find
the
standard
deviation
of
X
P

Y&
$D(X):
"é'"
=
>