UCLA
EE131A (KY)
1
EE 131A
Probability
Professor Kung Yao
Electrical Engineering Department
University of California, Los
Angeles
Lecture
Wed. June 4, 2008

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UCLA
EE131A (KY)
2
Verifying an empirical pdf (1)
•
We have studied analytical expressions of pdfs of
various continuous rv’s and pmf’s of discrete rv’s.
From an observed rv data, how do we accept/
reject a proposed pdf/pmf for modeling the
empirical pdf?
•
To use the Chi-Square Test for this purpose, we
need to define the Chi-Square rv and its pdf.
•
Let {X
1
, X
2
, …, X
n
} be n iid Gaussian rv’s of zero
mean and unit variance.
Then
Y =
S
2
(n) = X
1
2
+ X
2
2
+ … + X
n
2
,
(1)
is called a Chi-Square rv with a pdf defined by
f
Y
(y) = (y
(n-2)/2
e
-y/2
)/(2
n/2
Γ
(n/2)),
0 < y <
∞
, (2)